Rapid Modelling for Increasing Competitiveness: Tools and Mindset

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Rapid Modelling for Increasing Competitiveness

Gerald Reiner Editor

Rapid Modelling for Increasing Competitiveness Tools and Mindset

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Editor Prof. Dr. Gerald Reiner Institut de l’Entreprise (IENE) Faculté des Sciences Économiques Université de Neuchâtel Rue A.-L. Breguet 1 2000 Neuchâtel Switzerland [email protected]

ISBN 978-1-84882-747-9 e-ISBN 978-1-84882-748-6 DOI 10.1007/978-1-84882-748-6 Springer Dordrecht Heidelberg London New York British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Control Number: 2009929380 c Springer-Verlag London Limited 2009 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licenses issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of registered names, trademarks, etc., in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for general use. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Cover design: eStudioCalamar, Figueres/Berlin Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

Foreword

A Perspective on Two Decades of Rapid Modeling It is an honor for me to be asked to write a foreword to the Proceedings of the 1st Rapid Modeling Conference. In 1987, when I coined the term “Rapid Modeling” to denote queuing modeling of manufacturing systems, I never imagined that two decades later there would be an international conference devoted to this topic! I am delighted to see that there will be around 40 presentations at the conference by leading researchers from around the world, and about half of these presentations are represented by written papers published in this book. I congratulate the conference organizers and program committee on the success of their efforts to hold the first ever conference on Rapid Modeling. Attendees at this conference might find it interesting to learn about the history of the term Rapid Modeling in the context it is used here. During the fall of 1986 I was invited to a meeting at the Headquarters of the Society of Manufacturing Engineers (SME) in Dearborn, Michigan. By that time I had successfully demonstrated several industry applications of queuing network models at leading manufacturers in the USA. Although in principle the use of queuing networks to model manufacturing systems was well known in the OR/MS community and many papers had been published, the actual use of such models by manufacturing professionals was almost nonexistent. Instead, discrete-event simulation had been popularized through aggressive marketing by software companies, and if manufacturing managers wanted an analysis of their systems it was usually done by simulation. A few researchers, including myself, were trying to change this situation and include queuing models in the suite of tools used by manufacturing analysts. In the 1970s Professor Jim Solberg of Purdue had demonstrated that a Flexible Manufacturing System (FMS) could be modeled as a closed queuing network; he implemented a simple calculation on a hand calculator which he took with him as he visited manufacturers and impressed them with his quick predictions of throughput and bottlenecks. He called his model CAN-Q, for computer-aided network of queues. Motivated by his success, but finding his single-class model to be too simplistic, Dr. Rick Hildebrant (of the Draper Lab at MIT) and I developed an extension v

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of multiclass mean-value analysis (MVA) and implemented it in a software package called MVAQ. We demonstrated the practical value of queuing models by using MVAQ to quickly analyze and improve the throughput of an FMS at Hughes Aircraft Company during a production crisis (Suri and Hildebrant, 1984) - yes, the very same company formed by Howard Hughes that was seen in the recent movie called “The Aviator”! We then proceeded to use MVAQ at several FMS installations around the USA. However, I was not satisfied with the closed network model because FMSs were still rare and most manufacturing facilities operated more like open networks. At the same time Jackson networks were too limiting in their assumptions. So I homedin on the node decomposition approach developed and refined by Buzacott, Shanthikumar, Whitt and a few others, and in 1985 I wrote a software package called ManuPlan (in Fortran!). By the time of the 1986 meeting at SME, I had already demonstrated applications of ManuPlan not just by me, but by manufacturing analysts working at IBM, Alcoa, Digital Equipment Corporation, Pratt & Whitney Aircraft, and other companies - in other words, industry users were working with queuing models! Following this success, the software package was made more professional by a software company, Network Dynamics, Inc. (NDI). Eventually Dr. Gregory Diehl of NDI implemented it on a PC (the package was called ManuPlan II) and then greatly improved its interface to the latest version, MPX. A detailed perspective on these and many other developments in the area of queuing models of manufacturing systems can be found in the article, “From CAN-Q to MPX” (Suri et al, 1995). Anyway, let’s get back to the fall of 1986. The successes at IBM and other companies had been published in several articles and had caught the eye of the continuing education staff at SME. They wanted to know if I could teach a class to manufacturing professionals that would show them how to use queuing models to analyze manufacturing systems. The key question they had was, what would be the benefits of using this approach compared to simulation, and how could we convince people in industry to attend this class? (They didn’t think the term “queuing models” would do much to attract industry people!) At the SME meeting I explained that simulation models took weeks or months to build, debug and verify - in those days there was no interactive model-building software, and simulation models were built by writing detailed programming code. Further, even after the model was ready, it often took several hours for a single run. In other words, evaluation of a single set of decisions could take hours, and if you wanted to evaluate a number of alternatives it could take days or even weeks. I explained to the SME personnel that queuing models required only a few inputs, were easy to build, and just needed a few seconds to evaluate each scenario. As I went through these explanations, it suddenly dawned on me: what queuing models offered was a technique for rapid modeling of manufacturing systems - and the term Rapid Modeling was born! The SME team was convinced, and as a result I taught the first-ever continuing education class (known as a “Master Class” in Europe) on Rapid Modeling at SME Headquarters during April 28-30, 1987 (see Suri, 1987), also see Fig.1). Soon after that, I began using the acronym RMT for Rapid Modeling Technique and documented its advantages in

Foreword

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a 1988 article in Manufacturing Engineering (Suri, 1988). I also continued to teach Rapid Modeling classes at SME and at various manufacturing companies. In spite of these efforts, however, Rapid Modeling continued to play only a minor role in the modeling of manufacturing systems. This changed with a major advance in business strategy - and more significantly for this conference, when one of the members of this conference’s program committee invited me to collaborate with her on some projects. The year was 1988 and George Stalk had just published his article on Time-Based Competition (TBC). Professor Suzanne de Treville (then at the Helsinki University of Technology) invited me to Finland to work with Finnish companies on helping them reduce lead times and implement TBC, using the MPX software as an analysis tool. During these assignments we arrived at a critical insight: Rapid Modeling was the ideal tool to help companies reorganize their operations to reduce lead time. Static capacity models, or decision tools such as linear programming, did not show the tradeoffs between utilization and lead time; on the other hand simulation models were too complex and took too long to build, and managers could not wait that long to make time-sensitive strategic decisions. Rapid Modeling tools clearly showed senior managers the key tradeoffs involved and helped them to quickly justify and implement decisions to reduce their lead times (see De Treville, 1992 for examples of how Rapid Modeling benefited the projects in Finland).

Fig. 1 The first public use of the term Rapid Modeling at a continuing education class taught by the author at the Society of Manufacturing Engineers in 1987

From this point on, in our publications and classes we focused on the advantages of Rapid Modeling for lead time reduction (for example, see Suri, 1989). These ad-

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vantages were further emphasized with the development of Quick Response Manufacturing (QRM) - a refinement of TBC with a specific focus on manufacturing enterprises (Suri, 1998). For instance, at the Center for Quick Response Manufacturing, during our work with around 200 manufacturing companies during the past 15 years (see www.qrmcenter.org) we have found that Rapid Modeling is an invaluable tool to help companies reduce lead time and implement QRM. But enough about the past - let us look to the future. It is very encouraging to see an entire conference organized around the theme of Rapid Modeling, and to see that researchers from around the world will be presenting papers at this conference. Further, it is even more encouraging to see Rapid Modeling being extended beyond manufacturing systems - for example, to supply chain modeling, to container terminals and logistics management, to service processes, and even to venture capital firms and courts of law. All these events speak well for the future of Rapid Modeling. Finally, as one who promoted the Rapid Modeling concept as a tool to help manufacturing companies become more competitive, it is truly heartening to see that leading researchers in Europe have decided to use Rapid Modeling as a core concept in their EU project on “Keeping Jobs in Europe”(see Project Keeping Jobs In Europe, 2009). Once again, I congratulate the conference organizers and the program committee on the rich set of papers that have been put together here. I wish all the participants a fruitful conference, and I would also like to wish all these researchers success in the application of their Rapid Modeling concepts to many different fields. Neuchâtel, May 2009

Rajan Suri

References De Treville S (1992) Time is money. OR/MS Today 19(5):30–4 Project Keeping Jobs In Europe (2009) Keeping jobs in eu: Rapid modeling for the manufacturing and service industry. URL http://www2.unine.ch/iene-kje Suri R (1987) Rapid modeling techniques: Evaluating manufacturing system decisions. In: A Hands-on Course, SME World Headquarters, Dearborn, MI Suri R (1988) RMT puts manufacturing at the helm. Manufacturing Engineering February:41–44 Suri R (1989) Lead time reduction through rapid modeling. Manufacturing Systems 7:66–68 Suri R (1998) Quick response manufacturing: a companywide approach to reducing lead times. Productivity Press Suri R, Hildebrant R (1984) Modeling flexible manufacturing systems using meanvalue analysis. Journal of Manufacturing Systems Vol. 3(1):27–38 Suri R, Diehl G, de Treville S, Tomsicek M (1995) From CAN-Q to MPX: Evolution of queuing software for manufacturing. Interfaces 25(25):128–150

Preface

Rapid Modelling - Increasing Competitiveness - Tools and Mindset Despite the developments in the field of lead time reduction over the past 25 years, long lead times continue to have a negative impact on companies’ business results, i.e., customer dissatisfaction, loss of market shares, and missed opportunities to match supply and demand. Increased global competition requires companies to seek out new ways of responding to volatile demand and increased customer requirements for customization with continuously shorter lead times. Manufacturing companies, as well as service firms, in the developed economies are in the doldrums because low responsiveness make them vulnerable to low-cost competitors. Companies that are equipped for speed, with innovative processes, will outperform their slower competitors in many industries but the knowledge concerning lead time reduction, which has been developed globally, has yet to be combined into a unified theory. The purpose of this proceedings volume of selected papers presented at the 1st rapid modelling conference “Increasing Competitiveness - Tools and Mindset” is to give a state of the art overview about actual works in the field of rapid modelling in combination with lead time reduction. Furthermore, new developments will be discussed. In general, Rapid Modelling is based on queuing theory but other mathematical modelling techniques as well as simulation models to facilitate the transfer of knowledge from theory to application are of interest in this context as well. The interested reader, e.g., • researchers in the fields of – – – – –

operations management production management supply chain management operations research or industrial engineering as well as

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• practitioners with any connection to either – manufacturing or – service operations should have a good overview about what is going on in this field. The objective of this conference is to provide an international, multidisciplinary platform for researchers and practitioners to create and exchange knowledge on increasing competitiveness through speed. Lead time reduction (through techniques ranging from quick response manufacturing to lean production) is achieved through a mutually reinforcing combination of changed mindset and analytical tools. We accepted papers that contribute to these themes in the form of: • • • •

Theory Pieces and Reviews Modelling and Simulation Case Study and Action Research Survey and Longitudinal Research

Based on these research methods, the proceedings volume has been divided into four chapters and brings together papers which present different research methodologies. These papers are allocated based on their primary research methodology. All papers passed through a double-blind referee process to ensure their quality. Therefore, this book should serve as a valid source for research activities in this field. While the RMC09 (1st rapid modelling conference “Increasing Competitiveness - Tools and Mindset”) takes place at the University of Neuchâtel, located in the heart of the city of Neuchâtel, Switzerland, it is based on a collaboration with the project partners within our IAPP Project (No. 217891), see also http://www.unine.ch/ienekje. We are happy to have brought together authors from Algeria, Australia, Austria, Bahrain, Belgium, England, Finland, France, Germany, Hungary, Italy, Sweden, Switzerland and the United States of America.

Acknowledgement We would like to thank all those who contributed to the conference and this proceedings volume. First, we wish to thank all authors and presenters for their contribution. Furthermore, we appreciate the valuable help from the members of the international scientific board, the referees and our sponsors (see the Appendix for the appropriate lists). In particular, our gratitude goes to our support team at Enterprise Institute at the University of Neuchâtel, Gina Fiore Walder who organized all the major and minor aspects of this conference project. Ulf Richter, who handled the promotion process as well as the scientific referee process. Gina Fiore Walder, Yvan Nieto, Gil Gomes dos Santos supported by Arda Alp and Boualem Rabta handled the majority of the text reviews as well as the formating work with LaTex. Ronald Kurz created the logo

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of our conference and he took over the development of the conference homepage http://www.unine.ch/rmc09. Furthermore, we would like to give special thanks to Professor Rajan Suri, the founding director of the Center for Quick Response Manufacturing, University of Wisconsin-Madison, USA, who supported the development of our conference with valuable ideas, suggestions and hints. Furthermore, he authored the forward of this book based on his leading expertise in the field of Rapid Modelling as well as Quick Response Manufacturing. Finally, it has to be mentioned that the conference as well as the book are supported by the EU SEVENTH FRAMEWORK PROGRAMME - THE PEOPLE PROGRAMME - Industry-Academia Partnerships and Pathways Project (No. 217891) “How revolutionary queuing based modelling software helps keeping jobs in Europe. The creation of a lead time reduction software that increases industry competitiveness and supports academic research.” Neuchâtel, May 2009

Gerald Reiner

Contents

Part I Theory Pieces and Review 1

Managerial Decision Making and Lead Times: The Impact of Cognitive Illusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Suzanne de Treville, Ulrich Hoffrage and Jeffrey S. Petty

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Queueing Networks Modeling Software for Manufacturing . . . . . . . . 15 Boualem Rabta, Arda Alp and Gerald Reiner

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A Review of Decomposition Methods for Open Queueing Networks . 25 Boualem Rabta

Part II Modelling and Simulation 4

Parsimonious Modeling and Forecasting of Time Series drifted by Autoregressive Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Akram M. Chaudhry

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Forecast of the Traffic and Performance Evaluation of the BMT Container Terminal (Bejaia’s Harbor) . . . . . . . . . . . . . . . . . . . . . . . . . . 53 D. A¨ıssani, S. Adjabi, M. Cherfaoui, T. Benkhellat and N. Medjkoune

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A Dynamic Forecasting and Inventory Management Evaluation Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Johannes Fichtinger, Yvan Nieto and Gerald Reiner

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Performance Evaluation of Process Strategies Focussing on Lead Time Reduction Illustrated with an Existing Polymer Supply Chain Dominik Gläßer, Yvan Nieto and Gerald Reiner

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A Framework for Economic and Environmental Sustainability and Resilience of Supply Chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Heidrun Rosiˇc, Gerhard Bauer and Werner Jammernegg

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Contents

An Integrative Approach To Inventory Control . . . . . . . . . . . . . . . . . . 105 Philip Hedenstierna, Per Hilletofth and Olli-Pekka Hilmola

10 Rapid Modeling of Express Line Systems for Improving Waiting Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 Noémi Kalló and Tamás Koltai 11 Integrating Kanban Control with Advance Demand Information: Insights from an Analytical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Ananth Krishnamurthy and Deng Ge 12 Rapid Modelling in Manufacturing System Design Using Domain Specific Simulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Doug Love and Peter Ball 13 The Best of Both Worlds - Integrated Application of Analytic Methods and Simulation in Supply Chain Management . . . . . . . . . . . 155 Reinhold Schodl 14 Rapid Modeling In A Lean Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 Nico J. Vandaele and Inneke Van Nieuwenhuyse Part III Case Study and Action Research 15 The Impact of Lean Management on Business Level Performance and Competitiveness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 Krisztina Demeter, Dávid Losonci, Zsolt Matyusz and István Jenei 16 Reducing Service Process Lead-Time Through Inter-Organisational Process Coordination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 Henri Karppinen and Janne Huiskonen 17 Is There a Relationship Between VC Firm Business Process Flow Management and Investment Decisions? . . . . . . . . . . . . . . . . . . . . . . . . 209 Jeffrey S. Petty and Gerald Reiner 18 What Causes Prolonged Lead-Times in Courts of Law? . . . . . . . . . . . 221 Petra Pekkanen, Henri Karppinen and Timo Pirttilä 19 Logistics Clusters - How Regional Value Chains Speed Up Global Supply Chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 Ralf Elbert and Robert Schönberger Part IV Survey and Longitudinal Research 20 Measuring the Effects of Improvements in Operations Management . 249 Vedran Capkun, Ari-Pekka Hameri and Lawrence A. Weiss

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21 Managing Demand Through the Enablers of Flexibility: The Impact of Forecasting and Process Flow Management . . . . . . . . . . . . . 265 Matteo Kalchschmidt, Yvan Nieto and Gerald Reiner 22 Threats of Sourcing Locally Without a Strategic Approach: Impacts on Lead Time Performances . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 Ruggero Golini and Matteo Kalchschmidt 23 Improving Lead Times Through Collaboration With Supply Chain Partners: Evidence From Australian Manufacturing Firms . . . . . . . . 293 Prakash J. Singh A

International Scientific Board . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307

B

Sponsors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309

List of Contributors

Smail Adjabi Laboratory LAMOS, University of Béjaia, Targa Ouzemour, 6000 Béjaia, Algeria e-mail: [email protected] Djamil A¨ıssani Laboratory LAMOS, University of Béjaia, Targa Ouzemour, 6000 Béjaia, Algeria e-mail: lamos bejaia.hotmail.com Arda ALP Enterprise Institute, University of Neuchâtel, Rue A.L. Breguet 1, CH-2000 Neuchâtel, Switzerland e-mail: [email protected] Peter Ball Department of Manufacturing, Cranfield University, Cranfield, Bedford, MK43 0AL, U.K. e-mail: [email protected] Gerhard Bauer Vienna University of Economics and Business, Nordbergstraße 15, 1090 Vienna, Austria e-mail: [email protected] T. Benkhellat Laboratory LAMOS, University of Béjaia, Targa Ouzemour, 6000 Béjaia, Algeria Vedran Capkun HEC School of Management, 1, rue de la Liberation, 78351 Jouy-en-Josas cedex, France e-mail: [email protected] Akram M. Chaudhry College of Business Administration, University of Bahrain, P.O.Box #32038, Sakhir, Kingdom of Bahrain, Middle East xvii

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e-mail: [email protected], [email protected] M. Cherfaoui Laboratory LAMOS, University of Béjaia, Targa Ouzemour, 6000 Béjaia, Algeria Suzanne de Treville University of Lausanne, Faculty of Business and Economics, Internef 315, CH-1015 Lausanne, Switzerland e-mail: [email protected] Krisztina Demeter Department of Logistics and Supply Chain Management, Corvinus University of Budapest, Fovam ter 8, H-1093 Budapest, Hungary e-mail: [email protected] Ralf Elbert University of Technology Berlin, Chair of Logistics Services and Transportation, sec. H. 94 main building, Room H 9181, Straße des 17. Juni 135, 10623 Berlin, Germany e-mail: [email protected] Johannes Fichtinger Institute for Production Management, WU Vienna, Nordbergstraße 15, A-1090 Wien, Austria e-mail: [email protected] Deng Ge University of Wisconsin-Madison, Department of Industrial and Systems Engineering, 1513 University Avenue, Madison, WI 53706, USA e-mail: [email protected] Dominik Gläßer Institut de l’entreprise, Université de Neuchâtel, Rue A.-L. Breguet 1, CH-2000 Neuchâtel, Switzerland e-mail: [email protected] Ruggero Golini Department of Economics and Technology Management, Università degli Studi di Bergamo, Viale Marconi 5, 24044 Dalmine (BG), Italy e-mail: [email protected] Ari-Pekka Hameri Ecole des HEC, University of Lausanne, Internef, Lausanne 1015, Switzerland e-mail: [email protected] Philip Hedenstierna Logistics Research Group, University of Skövde, 541 28 Skövde, Sweden Per Hilletofth Logistic Research Group, University of Skövde, 541 28 Skövde, Sweden e-mail: [email protected]


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Olli-Pekka Hilmola Lappeenranta Univ. of Tech., Kouvola Unit, Prikaatintie 9, 45100 Kouvola, Finland Ulrich Hoffrage University of Lausanne, Faculty of Business and Economics, Internef 614, CH-1015 Lausanne, Switzerland e-mail: [email protected] Janne Huiskonen Department of Industrial Management, Lappeenranta University of Technology, P.O. Box 20, FIN-53851 Lappeenranta, Finland Werner Jammernegg Vienna University of Economics and Business, Nordbergstraße 15, 1090 Vienna, Austria e-mail: [email protected] István Jenei Department of Logistics and Supply Chain Management, Corvinus University of Budapest, Fovam ter 8, H-1093 Budapest, Hungary e-mail: [email protected] Matteo Kalchschmidt Department of Economics and Technology Management, Università di Bergamo, Viale Marconi 5, 24044 Dalmine, Italy e-mail: [email protected] Noémi Kalló Department of Management and Corporate Economics, Budapest University of Technology and Economics, Müegyetem rkp. 9. T. e´ p. IV. em., 1111 Budapest, Hungary e-mail: [email protected] Henri Karppinen Department of Industrial Management, Lappeenranta University of Technology, P.O. Box 20, FIN-53851 Lappeenranta, Finland e-mail: [email protected] Tamás Koltai Department of Management and Corporate Economics, Budapest University of Technology and Economics, Müegyetem rkp. 9. T. e´ p. IV. em., 1111 Budapest, Hungary e-mail: [email protected] Ananth Krishnamurthy University of Wisconsin-Madison, Department of Industrial and Systems Engineering, 1513 University Avenue, Madison, WI 53706, USA e-mail: [email protected]

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Dávid Losonci Department of Logistics and Supply Chain Management, Corvinus University of Budapest, Fovam ter 8, H-1093 Budapest, Hungary e-mail: ([email protected] Doug Love Aston Business School, Aston University, Birmingham, B4 7ET, U.K. e-mail: [email protected] Zsolt Matyusz Department of Logistics and Supply Chain Management, Corvinus University of Budapest, Fovam ter 8, H-1093 Budapest, Hungary e-mail: [email protected] N. Medjkoune Laboratory LAMOS, University of Béjaia, Targa Ouzemour, 6000 Béjaia, Algeria Yvan Nieto Institut de l’entreprise, Université de Neuchâtel, Rue A.-L. Breguet 1, CH-2000 Neuchâtel, Switzerland e-mail: [email protected] Petra Pekkanen Department of Industrial Management, Lappeenranta University of Technology, P.O. Box 20, FIN-53851 Lappeenranta, Finland e-mail: [email protected] Jeffrey S. Petty Lancer Callon Ltd., Suite 298, 56 Gloucester Road, UK-SW7 4UB London, United Kingdom e-mail: [email protected] Timo Pirttilä Department of Industrial Management, Lappeenranta University of Technology, P.O. Box 20, FIN-53851 Lappeenranta, Finland Boualem Rabta Enterprise Institute, University of Neuchatel, Rue A.-L. Breguet 1, CH-2000 Neuchatel, Switzerland e-mail: [email protected] Gerald Reiner Institut de l’entreprise, Université de Neuchâtel, Rue A.-L. Breguet 1, CH-2000 Neuchâtel, Switzerland e-mail: [email protected] Heidrun Rosiˇc Vienna University of Economics and Business, Nordbergstraße 15, 1090 Vienna, Austria e-mail: [email protected]


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Reinhold Schodl Capgemini Consulting, Lassallestr. 9b, 1020 Wien, Austria e-mail: : [email protected] Robert Schönberger University of Technology Darmstadt, Chair of Clusters & Value Chain,Darmstadt University of Technology, Hochschulstrasse 1, 64289 Darmstadt, Germany e-mail: [email protected] Prakash J. Singh Department of Management & Marketing, University of Melbourne-Parkville, 3010, Australia e-mail: [email protected] Nico J. Vandaele Research Center for Operations Management, Department of Decision Sciences and Information Management, K.U. 3000 Leuven, Belgium e-mail: [email protected] Inneke Van Nieuwenhuyse Research Center for Operations Management, Department of Decision Sciences and Information Management, K.U. 3000 Leuven, Belgium e-mail: [email protected] Lawrence A. Weiss McDonough School of Business, Georgetown University, Old North G01A, Washington, DC 20057-1147, USA e-mail: [email protected]

Part I

Theory Pieces and Review

Chapter 1

Managerial Decision Making and Lead Times: The Impact of Cognitive Illusions Suzanne de Treville, Ulrich Hoffrage and Jeffrey S. Petty

Abstract In this paper, we consider the impact of cognitive illusions on decision making in the operations management field, in areas ranging from product and process development to project management. Psychologists have studied the effects of overconfidence, the planning fallacy, illusions of control, anchoring, confirmation bias, hindsight bias, and associative memory illusions on individual judgment, thinking, and memory in many experiments, but little research has focused on operations management implications of these biases and illusions. Drawing on these psychological findings we discuss several of these cognitive illusions and their impact on operations managers, plant workers, technicians and engineers alike in a variety of operational settings. As in other contexts, these cognitive illusions are quite robust in operations management, but fortunately the impact of selected illusions can be substantially reduced through debiasing techniques. The examples discussed in this paper highlight the need for more operations-management-based research on the impact of cognitive illusions on decision making.

Suzanne de Treville University of Lausanne, Faculty of Business and Economics, Internef 315, CH-1015 Lausanne Téléphone : 021 692 33 41, e-mail: [email protected] Ulrich Hoffrage University of Lausanne, Faculty of Business and Economics, Internef 614, CH-1015 Lausanne e-mail: [email protected] Jeffrey S. Petty Lancer Callon Ltd., Suite 298, 56 Gloucester Road, UK-SW7 4UB London, e-mail: [email protected]

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Suzanne de Treville, Ulrich Hoffrage and Jeffrey S. Petty

1.1 Introduction People play an integral role in any operation, from process development to execution, assessment, and improvement. Because people are involved, most decisions exhibit some bias, as individuals use heuristics to simplify the decision-making process. Although such biases are not usually considered in managing and evaluating operations, they have a major impact on the decisions that are made, as well as how learning from decisions occurs. Cognitive illusions “lead to a perception, judgment, or memory that reliably deviates from reality” (Pohl 2004: 2). This deviation is referred to as a cognitive bias. Such illusions or biases happen randomly, tend to be robust and hard to avoid, and are difficult – sometimes impossible – to eliminate. There have been occasional references to the scarcity of literature on cognitive illusions or biases in the OM field (e.g., Mantel et al, in press; Schweitzer and Cachon, 2000). These papers refer to one or two cognitive biases, but do not present a large sample of biases that have been studied in the cognitive psychology literature.

1.2 Cognitive Illusions We begin with a bias that is fundamental to operations management: the planning fallacy (an example of overconfidence). We then consider the illusion of control, anchoring and adjustment, hindsight bias, confirmation bias, and associative memory illusion. We close with a brief discussion of debiasing techniques.

1.2.1 Overconfidence: The Planning Fallacy Overconfidence occurs when “our confidence in our judgments, inferences, or predictions is too high when compared to the corresponding accuracy (Hoffrage 2004: 235). One specific type of overconfidence is the planning fallacy, according to which “predicted completion times for specific future tasks tend to be more optimistic than can be justified by the actual completion times or by the predictors’ general beliefs about the amount of time such tasks usually take“ (Buehler et al 1994, 2002: 250). The planning fallacy results in substantial underestimation of timing or cost for a given project or task due to cognitive malfunctions (Buehler et al, 2002; Kahneman and Tversky, 1979; Lovallo and Kahneman, 2003). It is particularly likely for projects that are perceived as a linear set of well-understood tasks, which, however, is often not the case, as we describe shortly. The planning fallacy also has a temporal aspect: The more time we have to plan, the more overconfident we are and the more likely we are to underestimate the demands of the project (Sanna and Schwarz, 2004). Furthermore, the phenomenon increases with incentives (Buehler et al, 2002). This cognitive illusion is particu-

1 Managerial Decision Making and Lead Times: The Impact of Cognitive Illusions

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larly robust, occurring even when the decision-maker is completely aware of the phenomenon (Buehler et al, 2002). This phenomenon plays a fundamental role in operations management, in areas ranging from delivery to product and process development, to project management. Things always take longer than anyone expected, there is always a scramble to get things pulled together right before the final deadline, and no amount of planning or organization seems to eliminate this bias. Can insights from cognitive psychology inform operations management theory concerning how to improve lead time performance? Or, could operations management theory bring new insights to theory concerning the planning fallacy? Breaking projects into small pieces has been observed to keep projects more on schedule through creating the tension required to keep people focused on due dates (van Oorschot et al, 2002). While this might be feasible with the new product development projects studied by these authors, it would not work for repetitive operations (manufacturing or service). Furthermore, van Oorschot et al. noted that estimates for smaller project packages are more accurate, but the overall project time remains excessively long. Responding to lead times that are longer than expected by increasing our estimation of lead times leads to the “planning loop” (Suri, 1998); Longer estimates reduce the quality of forecasts, increasing mismatches between production and demand, placing additional demands on the system to respond to actual customer needs, resulting in higher utilization and longer lead times. This is consistent with the psychological realization mentioned early that the more time available, the worse the overconfidence. Historically, lead time estimation has been treated as a rational, linear computation. Suri (e.g., 1998) and Hopp and Spearman (1996) used queuing theory to illustrate the complexity of process dynamics, explaining part of the divergence between the expected simplicity and actual complexity of calculating lead times. These complex system dynamics may amplify the cognitive bias implied by the planning fallacy, thus partially explaining why in operations management we so consistently fail to get our lead times right. Furthermore, exploration of the interaction between the cognitive and computational aspects of lead time estimation may lead to new insights concerning this cognitive illusion. Most managers do not understand the impact of bottleneck utilization, lot size, layout, and system variability on lead time (Suri, 1994). As lead times not only increase but explode with utilization, it is not surprising that lead times exceed expectation in the majority of operations, especially given the common emphasis on maintaining high utilization. Therefore, an understanding of the mathematical principles that drive lead times might serve as a model for the cognitive processes involved in the planning fallacy.

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1.2.2 Illusion of Control Illusion of control occurs when an individual overestimates his or her personal influence on an outcome (Thompson, 2004). The illusion increases in magnitude with perceived skill, emphasis on success or failure, and need for a given outcome, as well as in contexts where skill coexists with luck, as people use random positive outcomes to increase their skill attributions (Langer and Roth, 1975). Consider an experienced worker who is choosing whether to follow process documents in completing a task. The illusion of control implies that the worker may believe that process outcomes will be better if he or she draws from experience and intuition rather than relying on the standard operating procedures (SOPs). Interestingly enough, this worker may well believe that other workers should follow the SOPs (for a discussion of worker insistence that co-workers follow SOPs, see Barker, 1993; Graham, 1995). Times when the worker has carried out a process change that has coincided with an improved yield (success, whether or not due to that change vs. normal process variability) will tend to increase this illusion of control. Polaroid’s efforts to introduce Statistical Process Control were hindered by workers’ illusions of control. Workers believed that process outcomes would be better if they were allowed to choose their own machine settings and make adjustments as they deemed necessary, rather than shutting down the machine and waiting for maintenance if process data indicated that the machine was going out of statistical control. This was in spite of data demonstrating substantially increased yields when machines were maintained to maximize consistency (Wheelwright et al, 1992). More generally, workers prey to the illusion of control are unlikely to embrace process standardization and documentation. Entrepreneurs may well demonstrate an illusion of control when it comes to developing the operations for their new venture. E Ink, for example, was a new venture originating from the MIT Media Lab that had invented an electronic ink, opening the door to “radio paper” and an eventual electronic newspaper that would have the look and feel of a traditional newspaper, but that would be updateable from newspaper headquarters. The attitude of the founders was that developing the new product was difficult, but that operations would be relatively easy-a classic illusion of control. Basic operations management problems (such as yield-to-yield variation) kept the company in survival mode for the better part of a decade (Yoffie and Mack, 2005). Had the founders made operations a priority from the start, they may well have been profitable many years earlier. The good news is that the illusion of control can be virtually eliminated by the intrusion of reality, which creates circumstances requiring individuals to systematically estimate the actual control that they have in a process (Thompson, 2004). In other words, before standardizing and documenting processes, or before designing new processes, it is worth carrying out an assessment exercise so that people have a clear understanding of their true abilities and control level.


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1.2.3 Anchoring and Hindsight Bias Anchoring and adjustment, that is, predicting or estimating relative to some anchor (Mussweiler et al, 2004), is a heuristic that is often evoked to explain cognitive biases that can be observed in various aspects of operations management. Anchors may be used individually when making decisions, or collectively across an organization as a benchmark for success or failure, often without regard for their relevance or impact on a given situation. In the operations management field we often use anchoring to make an operations strategy more powerful; Consider “Zero Defects” or “Zero Inventories,” “Justin-Time” or “lean production,” and “Six Sigma,” all of which have in common use of a keyword anchor that powerfully sets direction. The positive aspect of these anchors is that a direction or standard for the company has been established, it may, however, be set with such force that later efforts to moderate are unfruitful. Hopp and Spearman (1996), for example, described the confusion that resulted from use of the Zero Defects or Zero Inventories slogans, as companies responded by excessively slashing inventories or setting completely unrealistic quality objectives (as has also occurred as companies that should be striving for percent or parts-perthousand defects vainly strive for the ppm or even parts per billion implied by being six standard deviations from the process mean). The term lean is so powerful that companies may become overenthusiastic about removing slack resources (required for creativity, flexibility, or improvement efforts, e.g., Lawson, 2001) from processes (De Treville and Antonakis, 2006; Rinehart et al, 1997). Anchoring has been observed to move companies away from rational inventory policies (Schweitzer and Cachon, 2000), and to shift companies from constantly striving for improvement to just working toward meeting a set standard Tenbrunsel et al (e.g., that individuals stop seeking to save the environment and simply work to meet environmental standards, 2000). An interesting example of anchoring in the field of operations management comes from the shift in attitude toward the level of defects in a process over the past couple of decades. Twenty years ago, a classroom discussion of defect levels might include student claims that if the optimum is 10% defects and we are aiming for 2%, we are going to make less money than we should.“ Fast forward to today’s classroom, where a similar comment might beif the optimum is 300 parts per million (ppm) defects and we are aiming for 50 ppm” In other words, referring to percent vs. ppm anchors decision-makers as they set process improvement goals. Anchoring influences process experimentation. Consider a conveyor belt that carries product through a furnace that is limiting the overall capacity of the process. In thinking through how to increase throughput for the furnace operation, process development engineers may limit their experiments if they anchor their analysis to the existing process, rather than taking a new look at how the process is run. In the case of the conveyor, for example, it might be possible to almost double the output by stacking pieces on the belt, which would require both slowing the belt and increasing the temperature.

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On a larger scale, Campbell Soup anchored their process development activities to canned soup production in designing a line for microwaveable soups. This anchoring was not even questioned until a new project manager was brought in who had frozen food rather than canned soup experience, and was therefore free to break free from the anchor (unfortunately too late to save the project, Wheelwright and Gill, 1990).

1.2.4 Confirmation Bias “Whenever people search for, interpret, or remember information in such a way that the corroboration of a hypothesis becomes likely, independent of its truth, they show a confirmation bias.” (Oswald and Grosjean 2004: 93). Confirmation bias represents a “type of cognitive bias toward confirmation of the hypothesis under study. To compensate for this observed human tendency, the scientific method is constructed so that we must try to disprove our hypotheses” (Wikipedia, 2006). This type of bias becomes more likely when the “hypotheses tested are already established or are motivationally supported” (Oswald and Grosjean 2004: 93). Watkins and Bazerman (2003) described several disasters that would have been easily preventable had individuals not fallen prey to confirmation and related biases. “As managers estimate the likelihood of an event’s occurrence, they may overestimate the representativeness of a piece of information and draw inaccurate conclusions” (Bazerman, 2005). This also implies that information that is easily available may well have a greater impact on the decision made than it should: Whether decision-makers notice or ignore a piece of information often depends on how that information is presented (Mantel et al, in press). One of the early demonstrations of the confirmation bias came from an experiment in which subjects were shown the sequence 2, 4, 6, and asked to find the rule that generated the sequence. Subjects were to propose their own triples, learn from the experimenter whether the sequence conformed to the rule, and specified the rule as soon as they thought they had discovered it. The actual rule was “any ascending sequence.” Many subjects, however, assumed a rule of the form of n+2, and generated sequences of this form to confirm their guess. Such subjects were quite surprised to learn that their specified rule was wrong, in spite of the fact that they had only received positive and confirming feedback. Arriving at the correct rule required that subjects select examples that would disconfirm their beliefs, but this did not come naturally (Wason, 1960). Compare this phenomenon to an employee who has an idea about how to improve a process. As demonstrated by Wason, such an employee is more likely to suggest experiments to demonstrate that the idea works than to seek problems that may arise. Furthermore, implementation of insufficiently tested ideas is a primary source of production variability (Edelson and Bennett, 1998). The choice by Campbell Soup engineers to create a microwaveable soup process that resembled a canned soup line (argued in the preceding section to demonstrate


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anchoring) also provides an example of confirmation bias. Just as respondents in Wason (1960) experiment did not seek examples that would disconfirm the intuitive rule suggested by the initial sequence, so the Campbell Soup team made no apparent efforts to test their assumption that all soup lines should look like canned soup lines until the new project manager brought them a new model of reality (Wheelwright and Gill, 1990). There are many examples of confirmation biases in the operations management field. We mentioned previously how illusion of control led to unmanageable new processes in the Campbell Soup case (Wheelwright and Gill, 1990). The ability of these managers to dispel these illusions of control by an injection of reality was hindered by subsequent confirmation bias: Although it was clear that nothing was working as it should, management could not read the signals, nor did they perceive the costs to be excessive, and continued to invest in develop of the new processes. This example illustrates how cognitive illusions can coexist and reinforce each other. The confirmation bias emerges in decisions about outsourcing (for a discussion of confirmation-related biases in outsourcing, see Mantel et al, in press). Managers considering outsourcing have often already made up their minds about whether a supplier is capable of meeting their needs, so that they do not really consider the possibility that the supplier might fail. Confirmation bias can hinder communication and theory development, as opposing camps only consider information that supports their pet hypothesis, as can be seen in the case of lean production. A given factory is likely to have lean proponents and opponents, both of whom can produce substantial quantities of data supporting their viewpoint. The ability to really make use of conflicting data to falsify the opposing theory, however, appears to be the scarce supply (e.g., De Treville and Antonakis, 2006).

1.2.5 Associative Memory Illusion “In recollecting some target event from the past, people will often confuse events that happened before or after the target even with the event itself,” with some illusions involving remembrance of events that never actually occurred (Bartlett 1932/95; Roediger III and Gallo 2004: 309). In managing operations, memory plays an important role. When was the last time we did a furnace profile or maintained that machine? How has that supplier been performing over the past year? Does it seem like the process is stable? What has been going on with operators and repetitive strain injuries? The list goes on and on. The constant updating of memories plays an important role in adaptive learning, and is almost impossible to prevent or control (Roediger III and Gallo, 2004). That memory is constantly reconstructed based on our theories, beliefs, and subsequent experiences demonstrates the importance of excellent record-keeping and patience with those who remember differently. Associative memory illusions are related to illusions of change or stability (Wilson and Ross, 2004), referring to in-

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accurate comparisons of past and present states. Individuals, for example, often erroneously believe that improvement has occurred simply because of involvement in an improvement activity. Consider MacDuffie’s description of Ford’s improvement activities: “[Reporting forms] appear to be used more to report on the activity level of the subsystem group, to show that the required processes are being fulfilled, rather than to diagnose, systematically, the “root cause” and possible solutions to a problem. When a problem recurs, seldom is it reanalyzed, and rarely are earlier actions reassessed. With past activities already documented and reported, the key is to generate new documentation, to provide proof of continued activity. Thus, “continuous improvement” becomes less a process of incremental problem resolution than a process of energetic implementation of intuitively selected solutions” (MacDuffie, 1997, 185). In other words, the assumption of these managers is that activity = improvement, and this is seldom tested.

1.3 Debiasing Techniques Once cognitive biases have been identified, what debiasing techniques exist to reduce their impact? In this section we briefly examine some tools that may contribute to debiasing.

1.3.1 Inside or Outside Views In considering ways to reduce the planning fallacy, it is useful to differentiate between an inside (focusing on singular information) and an outside view (focusing on distributional information). One reduces the dominance of the singular (i.e., subjective probabilities for single cases) over the distributional approach (i.e., estimation of frequency distribution parameters) by eliciting predictions for aggregate sets of events rather than single cases. Asking for aggregate frequencies rather than singlecase estimates has proven to reduce or eliminate a number of cognitive illusions (Gigerenzer et al, in press). Unfortunately however, Buehler et al. (2002: 269) reported that using this method to debias the planning fallacy (asking questions in the form “In how many cases like this will you be able to keep the deadline?” rather than “What is your subjective probability of being able to keep the deadline?”) was not successful, speculating that it takes a sophisticated view to conceive of a given task as a sample of a more general reference class. It seems that participants adapt an inside view to make estimates about a given project, only then inferring a frequency response from this individual case. Beginning with an outside view to arrive at an inside view appears to be unnatural for average individuals.


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1.3.2 Consideration of Alternative Scenarios Evidence is inconclusive concerning the impact of asking individuals to consider alternative scenarios. On one hand, encouraging people to consider other, more pessimistic scenarios generally reduces overconfidence, both in knowledge and in prediction (Koriat et al, 1980). Not surprisingly, scenario planning has become popular as a forecasting tool in many business and organizational contexts (for a review, see Schoemaker, 1993). On the other hand, Buehler et al (2002) reported that in their studies the planning fallacy has resisted this technique, obviously because individuals’ best-guess predictions were overly influenced by the most optimistic scenarios, thereby downplaying the more pessimistic (and, unfortunately, often more realistic) scenarios.

1.3.3 Premortem Exercise We suggest that a technique called the Premortem exercise (Klein 2003: 98-101) may be more successful in overcoming or reducing the planning fallacy. This method starts with the assumption that a project or plan has failed. Not just a bit, but in a big way: It has turned out to be a catastrophe or disaster. Participants in the exercise take this failure as a given and provide reasons why it happened. This procedure relieves the participants from the (usually self-imposed) constraint that they must not say anything unpleasant, depressing, or potentially hurtful to their colleagues. The aim is to compile a long list of hidden assumptions that turned out to be wrong, or of weaknesses and key vulnerabilities in a plan. Once this list has been established, managers are enabled to take such “unforeseeable” events into account when planning, incorporating buffers and contingencies. Although in our experience the premortem technique has been quite successful in debiasing the planning fallacy, we are not aware of studies that have systematically explored its use.

1.3.4 Recall-Relevance Manipulation Getting participants to use their past experience to calibrate their time judgments has proven to be successful in empirical verification. Buehler et al (1994) required participants to first indicate the date and time they would finish a computer assignment if they finished it as far before its deadline as they typically completed assignments. In a second step, participants were asked to recall a plausible scenario from their past experience that would result in their completing the computer assignment at the typical time. Based on these estimations, they were to make predictions about completion times. This “recall-relevance” manipulation successfully reduced the optimistic bias constituting the planning fallacy.

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1.3.5 Incorporation of Lead Time Reduction Theory Combining an understanding of the mathematical relationships that drive lead times may be helpful in reducing the planning fallacy. Recall that the planning fallacy is particularly likely in situations where individuals perceive a project as a set of linear, straightforward tasks. Although operations often appear to be just such a set of linear and well-understood tasks, the underlying system dynamics are neither linear nor straightforward. We propose that a good understanding of the relationship between utilization, lot size, variability, and layout to lead time might encourage incorporation of a buffer at bottleneck operations, more attention to lot size and variability reduction, and implementation of layouts that support flow. Perhaps these operations management concepts will eventually inform the literature on the planning fallacy.

1.4 Conclusions This paper considered many of the biases and cognitive illusions which are relevant to the field of operations management and will continue to have an effect on operations as long as people are involved in the decision-making process. Cognitive psychologists have developed theories and conducted empirical research that can serve as a theoretical foundation for operations-based research. As demonstrated in the case examples cited, these biases occur in both start-up and established ventures, and across all levels of the companies. The planning fallacy and anchoring effect appear to dominate operations-related activities, but developing an understanding of each of the cognitive illusions presented in this paper in the operations management context may improve the quality of decisions in our field, as well as facilitate learning.

References Barker J (1993) Tightening the iron cage: Concertive control in self-managing teams. Administrative Science Quarterly 38:408–437 Bartlett F (1932/95) Remembering: A study in experimental and social psychology. Cambridge University Press Bazerman M (2005) Judgment in managerial decision making, 6th edn. John Wiley and Sons, New York Buehler R, Griffin D, Ross M (1994) Exploring the Planning Fallacy”: Why people underestimate their task completion times. Journal of Personality and Social Psychology 67:366–366 Buehler R, Griffin D, Ross M (2002) Inside the planning fallacy: The causes and consequences of optimistic time predictions. In: Gilovich DGT, Kahneman D


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(eds) Heuristics and Biases: The Psychology of Intuitive Judgement, Cambridge University Press, New York, pp 250–270 De Treville S, Antonakis J (2006) Could lean production job design be intrinsically motivating? Contextual, configurational, and levels-of-analysis issues. Journal of Operations Management 24(2):99–123 Edelson N, Bennett C (1998) Process discipline: How to maximize profitability and quality through manufacturing consistency. Quality Resources, New York Gigerenzer G, Hertwig R, Hoffrage U, Sedlmeier P (in press) Cognitive illusions. In: Smith P (ed) Handbook of experimental economics results, North Holland/Elsevier Press Graham L (1995) On the line at Subaru-Isuzu: The Japanese model and the American worker. ILR Press, Ithaca, NY Hoffrage U (2004) Overconfidence. In: Pohl R (ed) Cognitive Illusions, Psychology Press, Hove, East Sussex, pp 235–254 Hopp WJ, Spearman ML (1996) Factory Physics: Foundations of Manufacturing Management. Irvin Inc., Chicago Kahneman D, Tversky A (1979) Intuitive Prediction: Biases and Corrective Procedures. TIMS Studies in Management Science 12:313–327 Klein G (2003) The Power of Intuition. Currency/Doubleday Koriat A, Liechtenstein S, Fischhoff B (1980) Reasons for confidence. Journal of Experimental Psychology: Human Learning and Memory 6(2):107–118 Langer E, Roth J (1975) Heads I win, tails its chance: The illusion of control as a function of the sequence of outcomes in a purely chance task. Journal of Personality and Social Psychology 32(6):951–955 Lawson M (2001) In praise of slack: Time is of the essence. Academy of Management Executive 15(3):125–135 Lovallo D, Kahneman D (2003) Delusions of success. How optimism undermines executives’ decisions. Harvard Business Review 81(7):56 MacDuffie J (1997) The road to” Root Cause”: Shop-floor problem-solving at three auto assembly plants. Management Science 43(4):479–502 Mantel S, Tatikonda M, Liao Y (in press) A behavioral study of supply manager decision-making: Factors influencing make versus buy evaluation. Journal of Operations Management 24(6):822–838 Mussweiler T, Englich B, Strack F (2004) Anchoring Effect. In: Pohl R (ed) Cognitive illusions, Psychology Press (UK), Hove, East Sussex, pp 183–200 van Oorschot K, Bertrand J, Rutte C (2002) A longitudinal empirical study of the causes of lateness of new product development projects. URL http://www2.ipe.liu.se/rwg/igls/igls2002/Paper111.pdf Oswald M, Grosjean S (2004) Confirmation bias. In: Pohl R (ed) Cognitive Illusions, Psychology Press (UK), Hove, East Sussex, pp 79–96 Pohl R (2004) Introduction: Cognitive illusions. In: Pohl R (ed) Cognitive Illusions, Psychology Press (UK), Hove, East Sussex, pp 1–20 Rinehart J, Huxley C, Robertson D (1997) Just another car factory?: Lean production and its discontents. Cornell University Press, Ithaca, NY

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Roediger III H, Gallo D (2004) Associative memory illusions. In: Pohl R (ed) Cognitive Illusions, Psychology Press, East Sussex, pp 309–326 Sanna L, Schwarz N (2004) Integrating Temporal Biases. Psychological Science 15(7):474–481 Schoemaker P (1993) Multiple scenario development: Its conceptual and behavioral foundation. Strategic Management Journal 14(3):193–213 Schweitzer M, Cachon G (2000) Decision bias in the newsvendor problem with a known demand distribution: Experimental evidence. Management Science 46(3):404–420 Suri R (1994) Common misconceptions and blunders in implementing quick response manufacturing. Proceedings of the SME AUTOFACT ’94 Conference, Detroit, Michigan, November Suri R (1998) Quick response manufacturing: A companywide approach to reducing lead times. Productivity Press Tenbrunsel A, Wade-Benzoni K, Messick D, Bazerman M (2000) Understanding the influence of environmental standards on judgments and choices. Academy of Management Journal 43(5):854–866 Thompson S (2004) Illusions of control. In: Pohl R (ed) Cognitive Illusions, Psychology Press, Hove, East Sussex, pp 113–126 Wason P (1960) On the failure to eliminate hypotheses in a conceptual task. The Quarterly Journal of Experimental Psychology 12(3):129–140 Watkins M, Bazerman M (2003) Predictable surprises: The disasters you should have seen coming. Harvard Business Review 81(3):72–85 Wheelwright SC, Gill G (1990) Campbell Soup Company. In: Harvard Business School case 9-690-051, Cambridge, MA, p 23 Wheelwright SC, Bowen HK, Elliott B (1992) Process control at Polaroid. In: Harvard Business School case 9-693-047, Cambridge, MA, p 17 Wikipedia (2006) Confirmation bias. URL http://en.wikipedia.org /wiki/Confirmation bias. Wilson A, Ross M (2004) 21 Illusions of change or stability. In: Pohl R (ed) Cognitive Illustions, Psychology Press (UK), Hove, East Sussex, pp 379–396 Yoffie DB, Mack BJ (2005) E Ink in 2005. In: Harvard Business School case 9-705506, Cambridge, MA, p 24

Chapter 2

Queueing Networks Modeling Software for Manufacturing Boualem Rabta, Arda Alp and Gerald Reiner

Abstract This paper reviews the evolution of queueing networks software and its use in manufacturing. In particular, we will discuss two different groups of software tools. First, there are queueing networks software packages which require a good level of familiarity with the theory. In the other hand, there are some packages designed for manufacturing where the model development process is automated. Issues related to practical considerations will be adressed and recommendations will be given.

2.1 Introduction In a period of continuous change in global business environment, organizations, large and small, are finding it increasingly difficult to deal with, and adjust to the demands for such changes (Bosilj-Vuksic et al, 2007). In order to improve performance of a complex manufacturing system, the dynamic dependencies need to be understood well (e.g., utilization, variability, lead time, throughput, WIP, operating expenses, quality, etc). In this manner rapid modeling techniques like queueing theory, can be applied to improve such an understanding. For instance queueing Boualem Rabta Entreprise Institute, University of Neuchâtel, Rue A.L. Breguet 1, CH-2000 Neuchâtel, Switzerland. e-mail: [email protected] Arda Alp Entreprise Institute, University of Neuchâtel, Rue A.L. Breguet 1, CH-2000 Neuchâtel, Switzerland. e-mail: [email protected] Gerald Reiner Entreprise Institute, University of Neuchâtel, Rue A.L. Breguet 1, CH-2000 Neuchâtel, Switzerland. e-mail: [email protected]

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Boualem Rabta, Arda Alp and Gerald Reiner

networks are useful to model and measure the performance of manufacturing systems and also complex service processes. Apparently, queuing-theory-based software packages for manufacturing processes (e.g., MPX) automate model development process and help users (e.g. managers, academics) identify relatively easy analytical insights (Vokurka et al, 1996). Queuing software can be used by industrial analysts, managers, and educators. It is also a good tool to help students understand factory physics along with modeling and analysis techniques (see, e.g., de Treville and Van Ackere, 2006). Despite certain challenges over of queuing-theory-based modeling (e.g. need strong mathematical background, hard to maintain certain level of understanding on theories), training in queuing-theory-based modeling is likely to yield better competitiveness in lead time reduction (de Treville and Van Ackere, 2006). Business executives do not always make the best possible decisions. That is, managers can fail to understand the implications of mathematical laws and take actions that increase lead times (see, de Treville and Van Ackere, 2006; Suri, 1998). Complex real life service and manufacturing systems have a number of specific features as compared to ’simplistic cases’, posing important methodological challenges. Basic queuing theory provides key insights to practitioners but not complete and depth understanding of the system. Also the complexity of queuing theory based methods has caused companies to use other tools (e.g. simulation) rather than queuing theory. Finally, queuing theory becomes that much popular in academic and research areas, especially for operations modeling, because complexity and size of the real life problems can be reduced to relatively simple yet complex enough models. Compared to a similar simulation model, those will be in less detail, lacking transition behavior of the system but on the other hand simple and sufficient enough to make a decision (de Treville and Van Ackere, 2006). Basically, relatively simple and quick solutions are much more preferred as an initial system analysis or for quick decisions. The rest of this paper is organized as follows: In Section 22.2, we give a brief review of the evolution of queuing network theory, focusing on decomposition methods. In Section 22.3, we list selected queueing software packages. All of them are freely available for download on the Internet. Some manufacturing software packages based on queueing theory are presented in Section 2.4. Finally, we provide a conclusion and give recommendations in Section 2.5.

2.2 Queueing Networks Theory Queueing networks have been extensively studied in literature since Jackson’s seminal paper (Jackson, 1957). The first significant results were those of Jackson (Jackson, 1957, 1963) who showed that under special assumptions (exponnential interarrival and service times, markovian routing, first-come-first-served descipline,...) a queueing network may be analyzed by considering its stations each in isola-

2 Queueing Networks Modeling Software for Manufacturing

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tion (product form). Gordon and Newell showed that the product form solution also holds for closed queuing networks (i.e., networks where the number of jobs is fixed) with exponential interarrival and service durations (Gordon and Newell, 1967). Those results have been extended in (Baskett et al, 1975) and (Kelly, 1975) to other special cases (open, closed and mixed networks of queues with multiple job classes and different service disciplines). Since this kind of results was possible only under restrictive assumptions, other researchers tried to extend product form solutions to more general networks (decomposition methods). Several authors ( Kuehn (1979),Whitt (1983), Pujolle and Wu (1986), Gelenbe and Pujolle (1987) and Chylla (1986) among others) proposed decomposition procedures for open G/G/1 (G/G/m) queueing networks. Closed networks of queues have also been analyzed by decomposition (see, e.g., Marie, 1979). This approach has been modified in different ways since though (e.g., multiple job classes (Bitran and Tirupati, 1988; Whitt, 1994). In (Kim, 2004) and (Kim et al, 2005) it is shown that the classical Whitt’s decomposition method performs poorly in some situations (high variability and heavy traffic) and the innovations method is proposed as improvement, by replacing relations among squared coefficients of variability with approximate regression relationships among in the underlying point processes. This relationships allow to add information about correlations. It seems that the application of this method gives satisfactory results in various cases. However, there are still some situations where the existing tools fail. Other approaches which have been proposed include diffusion approximations (Reiser and Kobayashi, 1974) and Brownian approximations (Dai and Harrison, 1993; Harrison and Nguyen, 1990; Dai, 2002). Queueing theory is a well-known method for evaluating the performance of manufacturing systems under the influence of randomness (see, e.g., Buzacott and Shanthikumar, 1993; Suri, 1998). The randomness mainly comes from natural variability of interarrival times and service durations. Queueing networks modeling has its origins in manufacturing applications: Jackson’s papers (Jackson, 1957, 1963) targeted the analysis of job shops; a class of discrete manufacturing systems. Suri et al (1993) gave a detailed survey of analytical models for manufacturing including queueing network models. Govil and Fu (1999) presented a survey on the use of queueing theory in manufacturing. Shanthikumar et al (2007) surveyed applications of queuing networks theory for semiconductor manufacturing systems and discussed open problems.

2.3 Queueing Networks Software The developed theory motivated the development of many software packages for the analysis of queueing networks. These packages suppose a good level of familiarity with queueing theory. There are some early packages that were based on original algorithms. The Queueing Network Analyzer (QNA) has been proposed by Whitt as implementation of his two-node decomposition method (Whitt, 1983). QNET

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is another software package for performance analysis of queueing networks. It is the implementation of the analysis algorithm based on Brownian approximation of queueing networks (Dai and Harrison, 1993; Harrison and Nguyen, 1990) (motivated by heavy traffic theory). This package is written in text mode and its source code is available for free download. However, it seems that since mid 90s this software has not been rewritten and it is easy to guess that its use has remained very limited. See also, Govil and Fu (1999) for description of other queueing network packages. PEPSY-QNS /WinPEPSY: It has been developed at the University of ErlangenNurnberg in early 90s. It has a comfortable and easy to use graphical environment. This package includes more than 50 different analysis algorithms. The Windows version (WinPEPSY) has particular features : a user friendly graphical interface, a graphical network editor, charts for results... QNAT : The Queueing Network Analysis Tool (QNAT) is a Windows graphical package for analysing a wide variety of queueing networks. QNAT uses Mathematica as its computing platform and can handle general configurations of open and closed networks of both finite and infinite capacity queues. Incorporation of forkjoin nodes, multiclass customers, mixed customer classes and blocking mechanisms of different types are some of the other features available in this software tool. RAQS : Rapid Analysis of Queueing Systems (RAQS) is a Windows graphical queueing software (Kamath et al, 1995) based on the Whitt’s QNA method and its version in Segal and Whitt. (1989). It also implements decomposition algorithms for closed queuing networks and for tandem finite buffer queueing networks. It’s freely available for download. RAQS’ user interface provides less explanation for inexperienced users. Most probably, input and output interfaces are more suitable for experienced users who owns considerable amount of knowledge on basics of queueing theory. QTS : Queueing Theory Software, is written as Excel spreadsheet for solving a wide range of queueing models and other probability models (Markov chains, birth and death processes,...). The software is based on the textbook of Gross et al (2008). One advantage of this software is that the user has all-in-one model and several performance indicators (e.g., server utilization, mean number of jobs in the system and in the queue, mean waiting time in the system and in the queue...) in a simple sheet. JMT : The Java Modeling Tools is a free open source suite implementing several algorithms for the exact, asymptotic and simulative analysis of queueing network models. Models can be described either through wizard dialogs or with a graphical interface. The workload analysis tool is based on clustering techniques. The JMT tool is user-friendly including a visual design tool. Also, visual sliding buttons for simulation parameters (e.g. avg. arrival rate, avg. service time, buffer size and simulation time) makes what-if analysis easy for the user. Notice that those packages implement known (published) algorithms and are all freely available for download (some are open source, e.g., QTS, JMT). The difference is then in the number of implemented algorithms (the number of network types which can be analyzed), the user interface and the presentation of the results.


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Table 2.1 Download links for some free QN software WinPEPSY RAQS QST JMT

http://www7.informatik.uni-erlangen.de/ prbazan/pepsy/download.shtml http://www.okstate.edu/cocim/raqs/raqs.htm http://www.geocities.com/qtsplus/ (Also: http://qtsplus4calc.sourceforge.net/) http://jmt.sourceforge.net/

The important question is whether these software tools are practical and capable enough to satisfy the complex industry needs. Moreover, among the majority of functionalities that they offer, which one is suitable under which circumstances? When performing in a practical context the user of this kind of software is assumed to have an acceptable level of knowledge in queueing theory. The modeling has to be done separately and the results are generally given in a brute form. It is obvious that those drawbacks do not permit a wide use in a company given that managers are in general not queueing specialists.

2.4 Queueing Networks Software for Manufacturing Additionally the previous software tools, more specific software packages were designed for manufacturing based on queueing networks theory. Such modeling aid is automatic and embedded in the software and provides the user a unique ability to model the manufacturing system without worrying about the theoretical side. They are particularly suitable for use by industrials with little or no queueing knowledge. Snowdon and Ammons (1988) survey eight queueing network packages existing at that time. Some of the queueing network software packages are public domain while others are commercially sold by a software vendor. CAN-Q is a recursive algorithm for solving a product-form stochastic model of production systems (Co and Wysk, 1986) based on the results of Jackson and Gordon and Newell. A version of QNA supporting some features of manufacturing systems has also been proposed Segal and Whitt. (1989) but there are no indices that this package has been sold as commercial product or distributed for large use. Other early packages include Q-LOTS (Karmarkar et al, 1985), MANUPLAN (Suri et al, 1986) and Operations Planner (Jackman and Johnson, 1993). MANUPLAN includes an embedded dynamic model that is based on queueing network theory and provides common performance results such as WIP, tool utilization, production rate. The tool also provides trade-off analysis among inventory levels, flow times, reliability of the tools, etc. (Suri et al, 1986). MPX is perhaps the most popular software package in its category. It is the successor of MANUPLAN. Users greatly appreciate the speed of calculations and the ease of modeling despite of several missing improvements possibilities in its behavior and interface. The exact MPX’s algorithm is not published. Apparently, it uses the classical decomposition algorithm (Whitt, 1983) coupled to the operator/workstation algorithm (Suri et al, 1993) with some changes to support additional

20


features. It also provides a procedure to compute optimal lot sizes and transfer batch sizes. Still that the existing software model is quite generic and does not integrate high level of complexity. For instance, MPX does not provide support for some manufacturing features like finite capacity of buffers, service disciplines other than firstcome-first-served and dynamic lot sizing nor for some popular production systems (e.g., Kanban). On the other hand several industries prefer to use systems design software such as SAP-APO, IBM’s A-Team, etc., (Pinedo, 2002) and those generate their solution based on heuristics, relaxations or approximations different than queueing software solutions. However, usually those approaches have limitations. Their performance change based on certain settings and in general, user needs to complete several experiments to determine the most suitable algorithm. Additionally computation speed becomes one of the most important practical considerations. Instead of those all-inone, multi functional software designs, queueing software can provide quick and easy solutions while covering dynamics and related effects but not higher levels of system details (Suri et al, 1995).

2.5 Further Remarks When using queueing networks software in a practical setting, the resulting models are less accurate and detailed than simulation and give no insights into transition behavior, but they often suffice as decision support tools and can yield results that are useful in real-world applications (de Treville and Van Ackere, 2006). They provide a rapid and easy way to understand systems’ dynamics and predict their performance, in the opposition of complex simulation models which necessitate vast amount of modeling, advanced knowledge and computer time. It is important in today’s world to be able to rapidly evaluate different alternatives as manufacturing systems are in continuous change. This software packages are also an important tool for training and teaching the impact of some decisions on lead time and cost reduction. Queueing networks software is still has limited usage in practical complex manufacturing applications. It is not mature for practitioners how a queueing software can cover complex industry related constraints among with several tradeoffs regarding to several performance objectives. Other issues like data requirements may also be the cause. Software that passes the test of accuracy and detail can fail miserably in the field because it requires data beyond what are easily available (Suri et al, 1995). Those are basically limitations related to practical implications. Close contact between researchers and industrial users has been critical to the growth in use of the software. Emphasis on such contact, along with better linkages to operational systems, will ensure continued growth of manufacturing applications of queuing software (Suri et al, 1995). The use of the software in education may also help to enlarge its use in companies. When students realize the usefulness of


21

this tool, it becomes natural that they will use it after they join work in the industry or they become managers. When recognizing the importance of those tools and the opportunities they offer, the existing software packages are still limited in their modeling capabilities. It is important for software creators for enlarging the usability of their packages to offer support of different real manufacturing systems. While handing problems of modeling, a specified software design should be based on realistic assumptions (i.e. buffers capacity, priority rules, integration of forecasting and inventory policies). The combination of queueing networks analysis with statistical and optimization tools... can provide better solutions and attract more practical applications. The presentation of the computations’ output is also an important factor. Customizable reports and graphical charts help to better understand the results. It should be also possible for the software to provide some insights in the interpretation of the results and to warn the user about the limits of its performance (for example, MPX shows a warning when the utilization is very high saying that the results may not be accurate). Performance measures given by queueing packages are based on only steady-state value measurements given as the average values of such measures WIP, flow time. However, it can be desired to have variance (or variability) information about the output performance measures. Also, the provided average values are just approximate and it may be useful to provide trustable bounds for them. The success of a software package depends on many factors other than the accuracy of its computational method. Users look for a powerful tool with evidence of efficiency but also a user-friendly, easy-to-learn and well supported product (documentation and tutorial, demo version, consultancy/training course). The integration with other packages like spreadsheet packages, statistical packages, DBMS, legacy applications, ERP... is also a highly desired feature. Finally, the ability of the software to import/export data from/to other packages allows the users to gain in time and effort. Acknowledgements This work is supported by the SEVENTH FRAMEWORK PROGRAMME - THE PEOPLE PROGRAMME - Marie Curie Industry-Academia Partnerships and Pathways Project (No. 217891) ”Keeping jobs in Europe”

References Baskett F, Chandy K, Muntz R, Palacios F (1975) Open, closed and mixed networks of queues with different classes of customers. Journal of the ACM 22(2):248–260 Bitran G, Tirupati D (1988) Multiproduct queueing networks with deterministic rout-ing: Decomposition approach and the notion of interference. Management Science 34(1):75–100 Bosilj-Vuksic V, Ceric V, Hlupic V (2007) Criteria for the evaluation of business process simulation tools. Interdisciplinary Journal of Information, Knowledge and Management 2:73–88

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Buzacott JA, Shanthikumar JG (1993) Stochastic Models of Manufacturing Systems. Prentice-Hall, Englewood Cliffs, NJ Chylla P (1986) Zur Modellierung und approximativen Leistungsanalyse von Vielteilnehmer-Rechensystemen. Dessertation, Faculty for Mathematics and Computer Science, Technical university Munich Co HC, Wysk RA (1986) The robustness of can-q in modelling automated manufacturing systems. International journal of production research 24(6):1485–1503 Dai J, Harrison J (1993) The qnet method for two-moment analysis of closed manufacturing systems. Annals of Applied Probability 3(4):968–1012 Dai W (2002) A brownian model for multiclass queueing networks with finite buffers. Journal of Computational and Applied Mathematics 144(1–2):145–160 Gelenbe E, Pujolle G (1987) Introduction to queueing networks. John Wiley, Chichester Gordon W, Newell G (1967) Closed queueing systems with exponential servers. Operations Research 15(2):254–65 Govil M, Fu M (1999) Queueing theory in manufacturing : A survey. Journal of Manufacturing Systems 18(3):214–240 Gross D, Shortle JF, Thompson JM, Harris CM (2008) Fundamentals of Queueing Theory, 4th edn. John Wiley & Sons, Inc. Harrison JM, Nguyen V (1990) The qnet method for two-moment analysis of open queueing networks. Queueing Sytems 6(1):1–32 Jackman J, Johnson E (1993) The role of queueing network models in performance evaluation of manufacturing systems. Journal of the Operational Research Society 44(8):797–807 Jackson J (1963) Jobshop-like queueing systems. Management Science 10(1):131– 142 Jackson JR (1957) Networks of waiting lines. Operations Research 5(4):518–521 Kamath M, Sivaramakrishnan S, Shirhatti G (1995) Raqs: A software package to support instruction and research in queueing systems. Proceedings of 4th Industrial Engineering Research Conference, IIE, Norcross, GA pp 944–953 Karmarkar US, Kekre L, Freeman S (1985) Lotsizing and leadtime performance in a manufacturing cell. Interfaces 15(2):l–9 Kelly FP (1975) Networks of queues with customers of different types. Journal of Applied Probability 12(3):542–554 Kim S (2004) The heavy-traffic bottleneck phenomenon under splitting and superposition. European Journal of Operational Research 157(3):736–745 Kim S, Muralidharan R, O’Cinneide C (2005) Taking account of correlation between streams in queueing network approximations. Queueing Systems 49(3– 4):261–281 Kuehn PJ (1979) Approximate analysis of general networks by decomposition. IEEE Transactions on Communications 27(1):113–126 Marie R (1979) An approximate analytic method for general queueing networks. IEEE Transactions on Software Engineer 5(5):530–538 Pinedo M (2002) Scheduling: Theory, Algorithms, and Systems, 2nd edn. PrenticeHall Inc.


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Pujolle G, Wu A (1986) A solution for multiserver and multiclass open queueing networks. Information Systems and Operations Research 24(3):221–230 Reiser M, Kobayashi H (1974) Accuracy of diffusion approximations for some queueing networks. IBM Journal of Research and Development 18(2):110–124 Segal M, Whitt W (1989) A queueing network analyzer for manufacturing. Proceedings of the 12th International Teletraffic Congress, Torino, Italy, June 1988 pp 1146–1152 Shanthikumar J, Ding S, Zang M (2007) Queueing theory for semiconductor manufacturing systems : A survey and open problems. IEEE Transactions on Automation Science and Engiheering 4(4):513–522 Snowdon JL, Ammons JC (1988) A survey of queueing network packages for the analysis of manufacturing systems. Manufacturing Review 1(1):14–25 Suri R (1998) Quick Response Manufacturing. Productivity Press, Portland, OR Suri R, Diehl GW, Dean R (1986) Quick and easy manufacturing systems analysis using manuplan. Proceedings of the Spring HE Conference, Dallas, TX pp 195– 205 Suri R, Sanders J, Kamath M (1993) Performance Evaluation of Production Networks, vol 4: Logistics of Production and Inventory, Elsevier, pp 199–286 Suri R, Diehl GWW, de Treville S, Tomsicek MJ (1995) From can-q to mpx: Evolution of queuing software for manufacturing. Interfaces 25(5):128–150 de Treville S, Van Ackere A (2006) Equipping students to reduce lead times: The role of queuing-theory-based modeling. Interfaces 36(2):165–173 Vokurka RJ, Choobineh R, Vadi L (1996) A prototype expert system for the evaluation and selection of potential suppliers. International Journal of Operations & Production Management 16(12):106–127 Whitt W (1983) The queuing network analyzer. Bell Systems Technical Journal 62(9):2779–2815 Whitt W (1994) Towards better multi-class parametric-decomposition approximations for open queueing networks. Annals of Operations Research 48(3):221–248

Chapter 3

A Review of Decomposition Methods for Open Queueing Networks Boualem Rabta

Abstract Open queueing networks are useful for modeling and performance evaluation of complex systems such as computer systems, communication networks, production lines and manufacturing systems. Exact analytical results are available only in few situations with restricted assumptions. In the general case, feasible solutions can be obtained only through approximations. This paper reviews performance evaluation methods for open queueing systems with focus on decomposition methods.

3.1 Introduction Open queueing networks (OQN) are useful for modeling and performance evaluation of complex systems such as computer systems, communication networks, production lines and manufacturing systems. A Queueing network consists of several connected service stations. It is called open if customers can enter from outside and also r the system. A single station (or a node) queueing system consists of a queueing buffer of finite or infinite size and one or more identical servers. We will focus on unrestricted networks where each station has an infinite waiting capacity. Customers arrive from an external source to any station and wait for an available server. After being served, they move to the next station or leave the system. Performance evaluation of open queueing networks has been addressed through : • Exact methods : analytical results are available only in few situations with simple assumptions and particular topologies (Jackson networks). Many classes of networks have no known closed-form solutions. Boualem Rabta Entreprise Institute, University of Neuchatel, Rue A.-L. Breguet 1, CH-2000 Neuchatel (Switzerland) e-mail: [email protected]

25

26

Boualem Rabta

Fig. 3.1 An example of open queueing network (a) and a single station (b)

• Approximation methods including : diffusion approximations, mean value analysis, operational analysis, exponentialization approximations and decomposition methods. • Simulation and related techniques : This is perhaps, the most popular approach to evaluate the performance of queueing networks. Although more realistic and detailed, it can be cumbersome to optimize, and its accuracy is strongly dependent on the quality of the calibration data. First relevant analytical results for OQN were presented by Jackson (1957) who considered a special category (called thereafter Jackson networks) and showed that the joint distribution of the number of customers in the network is the product of the marginal distributions of the number of customers in each station (i.e., a product form solution). This kind of results allows us to analyze the network by considering each station individually. Product form results have been extended to a few situations (e.g. Kelly, 1975) but for general networks, product form solutions are not possible. Therefore, approximations are the only feasible solution. On the other hand, some networks have state spaces that are so large that certain analysis techniques, while theoretically possible, are impractical (Baldwin et al, 2003). The most frequently used approximation methods to analyze open queueing networks have been decomposition methods. According to this approach, the dimension of the network is reduced by breaking it down to sub-networks and analyzing each sub-network in isolation. The decomposition approach assumes that the sub-networks can be treated as being stochastically independent and that the input to each sub-network is a renewal process. Then, the analysis involves three basic steps : 1. decomposition of the network into sub-networks (in most cases, individual stations), 2. analysis of each sub-network and the interaction between the sub-networks, 3. recomposition of the results to compute the network performance.

3 A Review of Decomposition Methods for Open Queueing Networks

27

The parameters of each subnetwork depend on the state of other subnetworks and thus acknowledge the correlation with other subnetworks. The main difficulty lies in obtaining good approximations for these parameters. While the theory of single-station queues finds its origins in Erlang’s work on telecommunications at the beginning of the 20th century, the analysis of networks of queues began in the 1950s. Initial results appeared in Jackson (1954) who considered a system of two stations in tandem. Jackson (1957, 1963) analyzed a class of open queueing networks with Poisson external arrivals, exponential service times and Markovian routing of customers, and showed that the equilibrium probability distribution of customers could be obtained through node-by-node decomposition. Kelly (1975, 1976) extended Jackson’s work by including customers of several classes and different service disciplines. Similar results were presented by Barbour (1976). Baskett et al (1975) presented the most comprehensive results at the time for the classical models. First surveys of queueing network theory include Lemoine (1977) and Koenigsberg (1982). Lemoine discussed an overview of equilibrium results of general Jackson networks and the methodology which has been employed to obtain those results. Disney and Konig (1985) presented an extensive survey covering the seminal works of Jackson and the extensions of Kelly, including a bibliography of more than 300 references. Suri et al (1993) examined performance evaluation models for different manufacturing systems including production lines (tandem queues), assembly lines (arborescent queues), job-shops (OQN),... Buzacott and Shanthikumar (1992, 1993), Bitran and Dasu (1992) and Bitran and Morabito (1996) analyzed both performance evaluation models and optimization models for queueing networks. Bitran and Dasu (1992) discussed strategic, tactical and operational problems of manufacturing systems based on the OQN methodology, with a special attention to design and planning models for job-shops. Govil and Fu (1999) presented a survey on the use of queueing theory in manufacturing. Shanthikumar et al (2007) surveyed applications of queuing networks theory for semiconductor manufacturing systems and discussed open problems. Also, some software packages for the analysis of manufacturing systems are based on queueing networks theory. For instance, Manuplan and MPX (Suri et al, 1995) implement decomposition methods.

3.2 Jackson Networks 3.2.1 Single Class Jackson Networks When interarrival and service times are exponential, we refer to the network as a Jackson network. Here, the network is composed of several interconnected M/M/m stations with first–come–first–served (FCFS) discipline of service and an infinite queue capacity (n + 1 the number of stations in the system where station 0 rep-

28

Boualem Rabta

resents the external world to the network). Then, each station j is described by 3 parameters : The number of servers in the station, m j . The external arrival rate of customers to station j, λ0 j . The expected service rate, μ j . A customer who finishes the service at station i, moves to station j with probability ri j where, 0 ≤ ri j ≤ 1, ∀i, j = 0, .., n and ∑nj=0 ri j = 1, ∀i = 0, .., n. Thus, r0 j is the probability that a customers enters directly from outside to station j and r j0 is the probability that a customer leaves the network after just completing service at station j. Denote by λ j the overall arrival rate to station j and by λ the overall arrival rate to the whole network. By a result of Burke (1956) and Reich (1957) we know that the output of an M/M/m queue in equilibrium is Poisson with the same rate as the input process. Thus, n

λ j = λ0 j + ∑ ri j λi , ∀ j = 1..n,

(3.1)

i=1

is a system of linear equations known as traffic rate equations. The state of the system is defined as a vector x = (x1 , x2 , .., xn ) where x j is the number of customers in station j (customers in queue and in service). Under the assumption that the system reaches stationary regime, denote by π j (x j ) the probability of station j being in state x j and by π (x1 , x2 , .., xn ) the probability of the system being in state x = (x1 , x2 , .., xn ). Jackson (1957) showed that : n

π (x1 , x2 , .., xn ) = ∏ π j (x j ), j=1

with π j is the steady state distribution of the classical M/M/m j queueing system : ⎧ xj ⎪ ⎨ π j (0)m j ρ j if x j ≤ m j , xj! π j (x j ) = mj xj ⎪ ⎩ π j (0)m j ρ j if x j > m j , mj! where, ρ j is the expected utilization of station j, given as :

ρj =

∞

λj

∑ π j (k) = 1 − π j(0) = μ j m j , 0 ≤ ρ j < 1.

k=1

This result says that the network acts as if each station could be viewed as an independent M/M/m queue. In fact, it can be shown (Disney, 1981) that, in general, the actual internal flow in these kinds of networks is not Poisson (as long as there is any kind of feedback). Nevertheless, the previous relation still holds (see, Gross and Harris, 1998). The expected waiting time in queue at station j is the given by :


E(W j ) =

29

mj

ρ j (m j ρ j ) π j (0). λ j (1 − ρ j )2 m j !

The expected number of visits to station j : E(V j ) =

λj . λ0

(3.2)

where λ0 = ∑ni=1 λ0i . Finally, the expected lead time E(T ) (or cycle time) for an arbitrary customer, that is, the total time spent by a customer in the network from its arrival moment to its final departure, is given by : n 1 . E(T ) = ∑ E(V j ) E(W j ) + μj j=1 Note that the model in Jackson (1963) allows for arrival and service rates to depend on the state of the system. Whitt (1999) proposed a time-dependent and state-dependent generalization of a Jackson queueing network to model a telephone call center. For each station j, external arrivals λ j (t, x), service rates μ j (t, x) and routing probabilities r ji (t, x), i = 1, .., n depend upon the time t and the state x = (x1 , x2 , .., xn ) of the system. The Markovian structure makes it possible to obtain a time-dependent description of performance as the solution of a system of ordinary differential equations, but the network structure induces a very large number of equations, tending to make the analysis intractable. The author presented a framework for decomposition approximations by assuming the transition intensities of the underlying Markov chain to be of a product form.

3.2.2 Multiple Class Jackson Networks Baskett et al (1975) treated multiclass Jackson networks and obtained product form solutions for three service disciplines : processor sharing, ample service and last– come–first–served with preemptive resume servicing. Customers are allowed to switch classes after completing service at a station. The external input may be state dependent and service distributions can be of the phase type. They also considered multiple server first–come–first–served stations where customers of different classes have the same rate of exponentially distributed service times. See the discussion in Kleinrock (1976, Sec. 4.12). Reiser and Kobayashi (1974) generalized the result of Baskett et al. by assuming that customer routing transitions are characterized by a Markov chain decomposable into multiple subchains. Kelly (1975, 1976, 1979) also extended Jackson’s results to multiple class queueing networks. The type of a customer is allowed to influence his choice of path through the network and, under certain conditions, his service time distribution at each queue. Kelly’s model allows for different service disciplines. Even though, the equilibrium probability has a product form Disney and Konig (see also 1985).

30

Boualem Rabta

Let I be the number of customer classes. Customers of type i arrive to the network as a Poisson process with rate λ (i) and follow the route (i)

(i)

(i)

r1 , r2 , ..., r fi (i)

(i)

where r j is the j-th station visited by this type and r fi is the last station visited before leaving the system. At station j, customers have an exponentially distributed service requirement where requirements at stations visited by a customer of a particular class, are independent and those at all stations for all customers are mutually independent and independent of the arrival processes. If queue j contains k j customers then the expected service requirement for the (l) customer in position l is 1/μ j . Also, x j = (v jl , s jl ) (l = 1, ..., k j ) indicates that the l-th customer in the queue is of type v jl and is has reached the stage s jl along its route. X j = (x j1 , x j2 , ..., x jk j ) denotes the state of station j. The state of the network is represented by X = (X1 , X2 , ..., Xn ). It is then proved (Kelly, 1975; Disney and Konig, 1985) that the equilibrium distribution is given by : n

π (X) = ∏ π j (X j ) j=1

where

kj

π j (X j ) = B j ∏

α (v jl , s jl ) (l)

μj

l=1

Bj =

baj

∞

∑

(l) a a=0 ∏l=1 μ j I

,

,

fi

b j = ∑ ∑ α j (i, s), i=1 s=1

α j (i, s) =

(i)

λ (i) if rs = j, . 0 otherwise.

Let N j , ( j = 1, .., n) be the stationary queue lengths in equilibrium. their stationary probabilities are : k B jb j j

P Nj = k j = k . (l) j ∏l=1 μ j The equilibrium departure process of class i is a Poisson process with rate λ (i) and the departure processes of the different classes are mutually independent (Kelly, 1976). Although these results are interesting, practical implementations are difficult due to the size of the state space (Bitran and Morabito, 1996).


31

The previous model (Kelly, 1976) supposes deterministic routing. The general routing is considered in Kelly (1975). Based on the fact that nonnegative probability distributions can be well approximated by finite mixtures of gamma distributions, he further conjectured that many of his results can be extended to include general service time distributions. This conjuncture is proved by Barbour (1976). Gross and Harris (1998, Sec. 4.2.1) exposed a multiclass network where customers are served by m j exponential servers at station j, with the same service rate for all classes and first–come–first–served discipline. In this case, waiting time is the same for all customer classes. It is suggested to first solve the traffic equations separately for each customer class and then add the resulting arrival rates. Denote by (l) λ0 j the external arrival rate of customers of class l from outside to station j and let (l)

ri, j be the probability for a customer of class l to move to station j after completing (l)

the service at station i. Solving the traffic rate equation (3.1) yields λ j , j = 1, .., n for each class l; i.e., the overall arrival rate of customers of class l to station j. We (l) then obtain, λ j = ∑Il=1 λ j . Using M/M/m j results, we obtain the average number L j of customers in station j (the average waiting time can be obtained by Little’s formula). The average number of customers of class l in station j is then given by : (l)

Lj =

(l)

λj

(i)

∑Ii=1 λ j

L j.

3.3 Generalised Jackson Networks 3.3.1 Single Class Generalized Jackson Networks When the interarrival or service times (or both) are not exponential, we talk about a generalized Jackson network. Decomposition methods try to extend the independence between stations and Jackson’s product form solution to general open networks. The individual stations are analyzed as independent GI/G/m queues after approximating arrival processes by renewal processes. This approach involves : • Combination of the input of each station : arrivals from outside and from other stations are merged to produce an arrival flow to the station. • Analysis of each station as independent GI/G/m : compute performance measures and departures. • Splitting up departures from each station : decomposition of the overall departure flow into departure flows to other station and to outside. In general, distributions are specified by two first moments (the mean and the squared coefficient of variation). This approach was first proposed by Reiser and Kobayashi (1974) and improved by Sevcik et al (1977), Kuehn (1979), Shanthikumar and Buzacott (1981), Albin (1982), Whitt (1983a) among others.

32

Boualem Rabta

Fig. 3.2 Basic steps of decomposition

3.3.1.1 GI/G/1 Open Queueing Network Suppose we have n internal stations in the network with one server at each station. For a station j, external interarrival times a0 j and services times s j are independent and identically distributed (i.i.d) with general distributions. Define the following notations :

λ0 j expected external arrival rate. ca0 j scv (squared coefficient of variation) or variability of external interarrival time (ca0 j =

V(a0 j ) ). E(a0 j )2

μ j expected service rate (μ j = 1/E(s j )). cs j scv or variability of service time (cs j =

V(s j ) ). E(s j )2

After completing service at station i, a customer moves to station j with probability ri j or leaves the network with probability ri0 . Suppose that there is no immediate feedback (rii = 0, i = 1, .., n). Similarly to Jackson networks, we obtain exact (combined) expected arrival rates from the traffic rate equations (3.1). Necessary and sufficient conditions for stability of this network are well known. They are that at each station the total arrival rate must be less than the service rate. See Borovkov (1987) or, for a modern treatment and further references Dai (1995). Merging arrivals : The asymptotic method (Sevcik et al, 1977) and the stationary-interval method (Kuehn, 1979) may be used to determine ca j , i.e., the merged interarrival time variV(a )

ability (ca j = E(a j)2 , λ j = E(a1 j ) ). Moreover, the asymptotic method is asymptotij cally correct as ρ j → 1 (heavy traffic intensity) and the stationary-interval method is asymptotically correct when the arrival process tends to a Poisson process (Bitran and Morabito, 1996). Let cai j be the interarrival time variability at station j from station i. Based on the asymptotic method, ca j is a convex combination of cai j given by :


ca j =

n λ0 j λi j ca0 j + ∑ cai j . λj i=1 λ j

33

(3.3)

Albin (1982, 1984) suggested an approximation to ca j based on a convex combination between the previous value and the one obtained by the stationary interval method. Whitt (1983b) substituted the stationary interval method by a Poisson process and obtained : n λi j cai j + 1 − w j (3.4) ca j = w j ∑ i=0 λ j where wj =

1 1 + 4(1 − ρ j)2 (v j − 1) vj =

1 λi j ∑ni=0 ( λ j )2

Computing departures : The squared coefficient of variation cd j of the inter-departure stream from station j is computed by Marshall’s formula: cd j = ca j + 2ρ 2j cs j − 2ρ j (1 − ρ j )

E(W j ) . E(S j )

Using the Kraemer and Langenbach-Belz (1976) approximation for the expected waiting time E(W j ) at G/G/1 nodes, cd j = ρ 2j cs j + (1 − ρ 2j )ca j . Splitting departures : Under the assumption of Markovian routing, the departure stream from station j is split. The squared coefficient of variation cd ji of the departure stream from station j to station i is given by cd ji = r ji cd j + 1 − r ji. Analysis of single nodes : The expected waiting time E(W j ) in station j may be estimated by the KLB formula (Kraemer and Langenbach-Belz, 1976) : E(W j ) =

ρ j (ca j + cs j )g(ρ j , ca j , cs j ) , 2μ j (1 − ρ j )

34

Boualem Rabta

where,

g(ρ j , ca j , cs j ) =

exp 1

−2(1−ρ j )(1−ca j )2 3ρ j (ca j +cs j )

if ca j < 1, if ca j ≥ 1.

For other approximations of E(W j ) see, e.g., Shanthikumar and Buzacott (1981) and Buzacott and Shanthikumar (1993). The expected lead time E(T ) for a customer (including waiting times and service times) is given by : n 1 E(T ) = ∑ E(V j )(E(W j ) + ), μ j j=1 where E(V j ) is the expected number of visits to station j given by (3.2). 3.3.1.2 GI/G/m Open Queueing Network Suppose that in station j, there are m j (m j ≥ 1) identical servers. The following system of equations (Whitt, 1983a) allows us to determine ca j for each station : n

ca j = α j + ∑ cai βi j , for j = 1, .., n i=1

where

αj = 1 + wj

n

p0 j ca0 j − 1 + ∑

i=1

pi j (1 − ri j + ri j ρi2 yi )

βi j = w j pi j ri j (1 − ρi2) with w j is defined by (3.4) and pi j = yi = 1 +

λi j λi = ri j λj λj

max{csi , 0.2} − 1 . √ mi

The expressions for α j and βi j follow from considerations of the merging and splitting of customers streams and the impact of service time variability on the squared coefficient of traffic streams departing from a station, as opposed to that of incoming stream. The expected waiting time at station j is given by : E(W j ) =

ca j + cs j Wj 2


35

where W j is the expected waiting time for a M/M/m j queue. Many other approximations formulas for the mean waiting time in GI/G/m system are given in Bolch et al (2006, Sec.6.3.6). Creating and Combining Customers : The method described in this section allows for customers creation and combination by using a multiplication factor γ j at each station j (Whitt, 1983a). Eliminating immediate feedback : For those stations where r j j > 0 it is advantageous to consider the successive visits of a customer as one longer visit, that is, a customer gets its total service time continuously. The stations’ parameters are changed as follows (Kuehn, 1979) :

μ ∗j = μ j (1 − r j j ) cs∗2 j = r j j (1 − r j j )cs j ri∗j = ri j /(1 − r j j ), i = j. A proof of en exact analogy between stations with and without feedback with respect to the distribution of queue lengths and mean sojourn times was given by Takacs (1963) in the case of G/M/1 stations. The extension to general arrival processes is an approximation. It has been shown by simulation that this reconfiguration step of the network yields good accuracy, whereas the analysis without this step results in considerable inaccuracies (Kuehn, 1979). Further details may be found in Whitt (1983a,b) and Suri et al (1993). Manufacturing systems: To meet needs in the manufacturing environment, this method has been modified to represent machine breakdowns, batch service, changing lot sizes and product testing with associated repair and partial yields (Segal and Whitt, 1989). 3.3.1.3 The Bottleneck Phenomenon Suresh and Whitt (1990) showed that for tandem queues, for example, the original Whitt’s procedure performs well for all except the last station, which is a bottleneck. That is, the expected waiting time at the bottleneck station is underapproximated. The heavy-traffic bottleneck phenomenon can be described as a relatively large number in queue, observed when external arrivals are highly variable and a bot-

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Boualem Rabta

tleneck station is visited after jobs go through stations with moderate traffic (Kim, 2005). Whitt (1995) suggested an enhancement to the parametric-decomposition method for generalized Jackson networks. Instead of using a variability parameter for each arrival process, he proposed the use of a variability function for each arrival process; i.e., the variability parameter should be regarded as a function of the traffic intensity of a queue to which the arrival process might go. Dai et al (1994) proposed a hybrid method for analyzing generalized Jackson networks that employs both decomposition approximation and heavy traffic theory; the sequential bottleneck method, in which an open queueing network is decomposed in a set of groups of queues, i.e., not necessarily individual queues. 3.3.1.4 PH/PH/1(/K) Open Queueing Network Haverkort (1995, 1998) modified Whitt’s network by using PH/PH/1(/K) queues instead of GI/G/1 queues, so that the individual queues can be solved exactly using matrix-geometric techniques. In another step, he also allowed for the inclusion of finite capacity queues. Sadre et al (1999) extended this work by removing a few approximate steps in the decomposition procedure. In particular, they used exact results for the departure process of PH/PH/1/K queues, as first developed by Bocharov and Naumov (1986). 3.3.1.5 Open Queueing Network with Correlated Input As mentioned before, in most existing decomposition algorithms for open networks, the output of a queue is usually approximated as a renewal process, which becomes the arrival process to the next queue. Since the correlations of network traffic may have a considerable impact on performance measures, they must be captured to some extent by the employed traffic descriptors. Heindl (2001) considered a general tandem network where the internal traffic processes are described as semi-Markov processes (SMPs) and Markov modulated Poisson processes (MMPPs). Heindl and Telek (2002) presented a decomposition methodology based on Markovian arrival processes (MAPs), whose correlation structure is determined from the busy-period behavior of the upstream queues. The resulting compact MAPs in connection with sophisticated moment matching techniques allow an efficient decomposition of large queueing networks. Compared with a previous approach, the output approximation of MAP/PH/1(/K) queues - the crucial step in MAP-based decomposition - is refined in such a way that also higher moments of the number of customers in a busy period can be taken into account. Heindl et al (2006) constructed a Markovian arrival process of second order (MAP(2)) and showed numerically how their results can be used to efficiently decompose queueing networks. Kim et al (2005) proposed an improvement to Whitt’s method (called the innovations method) by replacing relations among squared coefficients of variability with approximate regression relationships among in the underlying point pro-


37

cesses. These relationships allow to add information on correlations between different streams. Kim (2004) combined the variability function and the innovations method in the context of the heavy traffic bottleneck phenomenon (Kim, 2004). Blacio˜glu et al (2008) proposed a tree-parameter renewal approximation to analyze the splitting and superposition of autocorrelated processes based on the work of Jagerman et al (2004). Two parameters capture information on the first and second order statistics of the original process and the third parameter captures the intricate behaviour that a superposition can exhibit.

3.3.2 Multiple Class Generalized Jackson Networks Whitt (1983a) proposed a procedure to aggregate all classes in a single one and utilize the single class model described above. In this way the original multiple class model is reduced to a single aggregate open network. After the analysis of the aggregate class model, the performance measures for each class are estimated individually.In many cases this aggregation step works quite well, but in some cases it does not (Whitt, 1994). Bitran and Tirupati (1988) considered an open queueing network with multiple customer classes, deterministic routing and generally distributed arrivals and service times. They pointed out that the splitting operation in the original Whitt’s procedure may not perform well due to the existence of interference among classes. Their approximation is based on the two–class case, by aggregating all classes except the one of interest into one where the aggregate arrivals of class 2 is assumed to follow a Poisson processes. Their procedure provides dramatic improvements in accuracy in some cases (Whitt, 1994). As an extension to the approximations by Bitran and Tirupati (1988) and Whitt (1994) developed methods for approximately characterizing the departure process of each customer class from a multi-class single-server queue ∑(GIi /GIi )/1 with a non-Poisson renewal arrival process and a non-exponential service-time distribution for each class, unlimited waiting space and the FCFS service discipline. The results are used for improving parametric-decomposition approximations for analyzing non-Markov open queueing networks with multiple classes. The effect of class-dependent service times is also considered there. Whitt used different approaches : an extension of Bitran and Tirupati’s formula (based on batch poisson and batch deterministic processes) and a heuristic hybrid approximation based on the results for the limiting case where a server is continuously busy. Caldentey (2001) presented an approximation method to compute the squared coefficient of variation of the departure stream from a multiclass queueing system generalizing the results of Bitran and Tirupati (1988) and Whitt (1994). Kim (2005) considered a multiclass deterministic routing queueing network with highly variable arrivals. He pointed out that the previous procedures of Bitran and Tirupati (1988) and Whitt (1994), may not be accurate under high variability as-

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Boualem Rabta

sumption. He proposed refinements to those results based on Whitt’s variability functions.

3.4 Other Classes of Networks 3.4.1 Infinite Server Networks Harrison and Lemoine (1981) considered networks of queues with an infinite number of servers at each station. They pointed out that independent motions of customers in the system, which are characteristic of infinite-server networks, lead in a simple way to time-dependent distributions of state, and thence to steady-state distributions. Moreover, these steady-state distributions often exhibit an invariance with regard to distributions of service in the network. Massey and Whitt (1993) considered a network of infinite-server queues with nonstationary Poisson input. As a motivating application, they cited wireless (or mobile cellular) telecommunications systems.Their model appears as a highly idealized model, which initially ignores resource constraints. The different queues represent cells. Call originations are modeled as a nonhomogeneous Poisson process, with the nonhomogeneity capturing the important time-of-day effect.

3.4.2 Batch Movement Networks In real life, many applications feature simultaneous job transitions. For example, in manufacturing, parts are often processed and transported in batches. Batch queuing networks have been considered by Kelly (1979) and subsequently Whittle (1986) and Pollett (1987). Miyazawa and Taylor (1997) proposed a class of batch arrival batch service continuous-time open queueing networks with batch movements. A requested number of customers is simultaneously served at a node, and transferred to another node as, possibly, a batch of different size, if there are sufficient customers there; the node is emptied otherwise. Their model assumes a Markovian setting for the arrival process, service times and routing, where batch sizes are generally distributed. The authors introduced an extra batches arrival process while nodes are empty and showed that the stationary distribution of the queue length has a geometric product form over the nodes if and only if certain conditions are satisfied for the extra arrivals and under a stability condition. The correspondence between batch–movement queueing networks and single– movement queueing networks has also been discussed in Coleman et al (1997) for class of networks having product–form solutions.


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Meng and Heragu (2004) proposed an extention to the classical decomposition algorithm Whitt (1983a) to handle transfer batch size change between stations. They consider only deterministic routing where transfer batch sizes are also deterministic. Acknowledgements This work is supported by the SEVENTH FRAMEWORK PROGRAMME - THE PEOPLE PROGRAMME - Marie Curie Industry-Academia Partnerships and Pathways Project (No. 217891) ”Keeping jobs in Europe”

References Albin SL (1982) On poisson approximations for superposition arrival processes in queues. Management Science 28(2):126–137 Albin SL (1984) Approximating a point process by a renewal process, ii: Superposition arrival processes to queues. Operations Research 32(5):1133–1162 Baldwin R, Davis IV N, Midkiff S, Kobza J (2003) Queueing network analysis: concepts, terminology, and methods. Journal of Systems and Software 66(2):99– 117 Barbour A (1976) Networks of queues and the method of stages. Advances in Applied Probability 8(3):584–591 Baskett F, Chandy K, Muntz R, Palacios F (1975) Open, closed and mixed networks of queues with different classes of customers. Journal of the ACM 22(2):248–260, DOI http://doi.acm.org/10.1145/321879.321887 Bitran G, Morabito R (1996) Open queueing networks : Optimization and performance evaluation models for discrete manufacturing systems. Production and Operations Management 51(2–4):163–193 Bitran G, Tirupati D (1988) Multiproduct queueing networks with deterministic routing: Decomposition approach and the notion of interference. Management Science 34(1):75–100 Bitran GR, Dasu S (1992) A review of open queueing network models of manufacturing systems. Queueing Systems 12(1-2):95–134 Blacio˜glu B, Jagerman D, Altiok T (2008) Merging and splitting autocorrelated arrival processes and impact on queueing performance. Performance Evaluation 65(9):653–669 Bocharov P, Naumov V (1986) Matrix-geometric stationary distribution for the PH/PH/1/r, queue. Elektronische Informationsverarbeitung und Kybernetik 22(4):179–186 Bolch G, Greiner S, de Meer H, Trivedi K (2006) Queueing Networks and Markov Chains : Modeling and Performance Evaluation with Computer Science Applications, 2nd edn. Wiley, New York Borovkov AA (1987) Limit theorems for queueing networks. i. Theory Probab Appl 31(3):413–427 Burke P (1956) The output of a queueing system. Operations Research 4(6):699– 704

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Buzacott JA, Shanthikumar JG (1992) Design of manufacturing systems using queueing models. Queueing Systems 12(1–2):135–213 Buzacott JA, Shanthikumar JG (1993) Stochastic models of manufacturing systems. Prentice-Hall, Englewood Cliffs, NJ Caldentey R (2001) Approximations for multi-class departure processes. Queueing Systems 38(2):205–212 Coleman J, Henderson W, Pearce C, Taylor P (1997) A correspondence between product-form batch-movement queueing networks and single-movement networks. Journal of Applied Probability 34(1):160–175 Dai J (1995) On positive recurrence of multiclass queueing networks: A unified approach via fluid limit models. Annals of Applied Probability 5(1):49–77 Dai J, Nguyen V, Reiman M (1994) Sequential bottleneck decomposition: an approximation method for generalised jackson networks. Operations Research 42(1):119–136 Disney RL (1981) Queueing networks. Proceedings of AMS Symposia in Applied Mathematics 25:53–83 Disney RL, Konig D (1985) Queueing networks: A survey of their random processes. SIAM Review 27(3):335–403 Govil M, Fu M (1999) Queueing theory in manufacturing : A survey. Journal of Manufacturing Systems 18(3):214–240 Gross D, Harris M (1998) Fundamentals of Queueing Theory, 3rd edn. Wiley, New York Harrison J, Lemoine A (1981) A note on networks of infinite-server queues. Journal of Applied Probability 18(2):561–567 Haverkort B (1995) Approximate analysis of networks of PH/PH/1/K, queues: Theory & tool support. In: MMB ’95: Proceedings of the 8th International Conference on Modelling Techniques and Tools for Computer Performance Evaluation, isbn: 3-540-60300-X, Springer-Verlag, London, UK, pp 239–253 Haverkort B (1998) Approximate analysis of networks of PH/PH/1/K, queues with customer losses: Test results. Annals of Operations Research 79(0):271–291 Heindl A (2001) Decomposition of general tandem queueing networks with mmpp input. Performance Evaluation 44(1-4):5–23 Heindl A, Telek M (2002) Output models of MAP/PH/1(/K) queues for an efficient network decomposition. Performance Evaluation 49(1–4):321–339 Heindl A, Mitchell K, van de Liefvoort A (2006) Correlation bounds for secondorder maps with application to queueing network decomposition. Performance Evaluation 63(6):553–577 Jackson JR (1957) Networks of waiting lines. Operations Research 5(4):518–521 Jackson JR (1963) Job shop-like queueing systems. Management Science 10(1):131–142 Jackson RRP (1954) Queueing systems with phase type service. OR 5(4):109–120 Jagerman D, Bolcio˜glu B, Altiok T, Melamed B (2004) Mean waiting time approximations in the g/g/1 queue. Queueing Systems 46(3):481–506 Kelly FP (1975) Networks of queues with customers of different types. Journal of Applied Probability 12(3):542–554


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Kelly FP (1976) Networks of queues. Journal of Applied Probability 8(2):416–432 Kelly FP (1979) Reversibility and Stochastic Processes. Wiley, NY Kim S (2004) The heavy-traffic bottleneck phenomenon under splitting and superposition. European Journal of Operational Research 157(3):736–745 Kim S (2005) Approximation of multiclass queueing networks with highly variable arrivals under deterministic routing. Naval Research Logistics 52(5):399–408 Kim S, Muralidharan R, O’Cinneide C (2005) Taking account of correlation between streams in queueing network approximations. Queueing Systems 49(3– 4):261–281 Kleinrock L (1976) Queueing systems, Vol. II : Computer applications. Wiley, New York Koenigsberg E (1982) Twenty five years of cyclic queues and closed queue networks: A review. The Journal of the Operational Research Society 33(7):605–619 Kraemer W, Langenbach-Belz M (1976) Approximate formulae for the delay in the queueing system gi/g/1. Proceedings of the 8th International Teletraffic Congress, Melbourne 235:1–8 Kuehn PJ (1979) Approximate analysis of general queuing networks by decomposition. IEEE Transactions on Communications 27(1):113–126 Lemoine AJ (1977) Networks of queues - a survey of equilibrium analysis. Management Science 24(4):464–481 Massey WA, Whitt W (1993) Networks of infinite-server queues with nonstationary poisson input. Queueing Systems 13(1–3):183–250 Meng G, Heragu SS (2004) Batch size modeling in a multi-item, discrete manufacturing system via an open queuing network. IIE Transactions 36(8):743–753 Miyazawa M, Taylor P (1997) A geometric product-form distribution for a queueing network with non-standard batch arrivals and batch transfers. Advances in Applied Probability 29(2):523–544 Pollett PK (1987) Preserving partial balance in continuous-time markov chains. Advances in Applied Probability 19(2):431–453 Reich E (1957) Waiting times when queues are in tandem. Annals of Mathematical Statistics 28(3):768–773 Reiser M, Kobayashi H (1974) Accuracy of the diffusion approximation for some queuing systems. IBM Journal of Research and Development 18(2):110–124 Sadre R, Haverkort B, Ost A (1999) An efficient and accurate decomposition method for open finite- and infinite-buffer queueing networks. In W Stewart and B Plateau, editors, Proceedings 3rd International Workshop on Numerical Solution of Markov Chains p 120 Segal M, Whitt W (1989) A queueing network analyser for manufacturing. Teletraffic Science for New Cost-Effective Systems, Networks and Services, Proceedings of ITC 12 (ed M Bonatti), North-Holland, Amsterdam pp 1146–1152 Sevcik KC, Levy AI, Tripathi SK, Zahorjan JL (1977) Improving approximations of aggregated queueing network systems. Computer Performance (eds K Chandy and M Reiser), North-Holland pp 1–22

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Shanthikumar J, Ding S, Zang M (2007) Queueing theory for semiconductor manufacturing systems : A survey and open problems. IEEE Transactions on Automation Science and Engiheering 4(4):513–522 Shanthikumar JG, Buzacott JA (1981) Open queueing network models of dynamic job shops. International Journal of Production Research 19(3):255–266, DOI 10.1080/00207548108956652 Suresh S, Whitt W (1990) The heavy-traffic bottleneck phenomenon in open queueing networks. Operations Research Letters 9(6):355–362 Suri R, Sanders JL, Kamath M (1993) Performance evaluation of production networks, vol 4. Elsevier, North-Holland,Amsterdam Suri R, Diehl GWW, de Treville S, Tomsicek MJ (1995) From can-q to mpx: Evolution of queuing software for manufacturing. Interfaces 25(5):128–150 Takacs L (1963) A single server queue with feedback. BSTJ 42:505–519 Whitt W (1983a) The queueing network analyzer. The Bell System technical journal 62(9):2779–2815 Whitt W (1983b) Performance of the queueing network analyzer. The Bell System technical journal 62(9):2817–2843 Whitt W (1994) Towards better multi-class parametric-decomposition approximations for open queueing networks. Annals of Operations Research 48(3):221–248 Whitt W (1995) Variability functions for parametric-decomposition approximations of queueing networks. Management Science 41(10):1704–1715 Whitt W (1999) Decomposition approximations for time-dependent markovian queueing networks. Operations Research Letters 24(3):97–103, DOI http://dx.doi.org/10.1016/S0167-6377(99)00007-3 Whittle P (1986) Systems in Stochastic Equilibrium. Wiley, London

Part II

Modelling and Simulation

Chapter 4

Parsimonious Modeling and Forecasting of Time Series drifted by Autoregressive Noise Akram M. Chaudhry

Abstract This paper addresses issue of modeling, analysis and forecasting of time series drifted by autoregressive noise and finding its optimal solution by extending a conventional linear growth model with an autoregressive component. This additional component is designed to take care of high frequencies of autoregressive noise drift without influencing the low frequencies of the linear trend and compromising on parsimonious nature of the model. The parameters of this model are then optimally estimated through the self updating recursive equations using Bayesian priors. For identification of autoregressive order of noise and estimation of its coefficients ATS procedure of Akram (2001) is employed. Further, for unknown variance of observations an on-line variance learning and estimation procedure is discussed. To demonstrate practical aspects of the model some examples are given and for generation of short, medium and long term forecasts in one go an appropriate forecast function is given.

4.1 Introduction In many economic, financial and physical phenomena time series drifted by autoregressive noise are observed. For analysis of such series numerous simple to complex models had been proposed by researchers. Most of these models are meant for either short term forecasts or medium term or long term forecasts only. Very few of these models generate three types of forecasts in one go. To obtain all these types of forecasts, usually, three different models are employed using different model settings. These forecasts are then joined or/combined to visualize them in one sequence over short to long term time horizon. To do so some sort of alignment is made by the foreAkram M. Chaudhry, Associate Professor College of Business Administration, University of Bahrain-P.O.Box #32038, Sakhir, Kingdom of Bahrain, Middle East, Contact: (+973) 39171071(Mobile), 17438586(Office), 17642281(Res.) e-mail: [email protected], [email protected], [email protected]

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casters by underestimating or/and overestimating the actual forecasts at the joints. By doing so some accuracy of forecasts is sacrificed resulting in heuristic rather than optimum forecasts. Further, for identification of an order of auto-regression of noise terms parametric techniques, such as, Akaike (1973) and Bohlin (1978) are frequently used. These techniques are known to be cumbersome and some time ambiguous. To overcome these problems, a parsimonious linear growth model having an additional drift component is presented. This additional component that takes care of auto-regression in noise component can be easily modeled and re-parameterized if need arises. Before discussing extended model, let us go through a conventional linear growth model of Harrison and Akram (1983) meant for taking care of low frequencies of trend, bearing white noise.

4.1.1 Conventional Linear Growth Model For analysis and forecasting of time series {yt }t=1,2,,T bearing white noise {δt }t=1,2,,T the conventional linear growth model at time t is locally defined as: Yt = f θt + δt

θt = Gθt−1 + wt Where: f = (1×n) vector of unknown stochastic parameters. θt = (n×l) vector of unknown stochastic parameters. G = (n × n) matrix, called, state or transition matrix, of nnumber of nonzero eigenvalues {λi }i=1,...,n . δt is an observation noise, assumed to be normally distributed with mean zero and some known constant variance. wt = (n × 1) vector of parameter noise, assumed to be normally distributed with mean zero and a constant known variance-covariance matrix W = diag(W 1, . . . ,W n), the components of which are as defined by Harrison and Akram (1983). 4.1.1.1 Example 1 In case of a second order (n = 2) model, the above components of the model, in canonical form, at time t are: f= 10

θt = (θ1 , θ2 ) , where the parameter θ1 is the level of underlying process of time series and θ2 is the growth parameter.

4 Parsimonious Modeling and Forecasting of Time Series

47

G = {gi j }i, j=1,2 is a 2 × 2 transition matrix having non zero eigenvalues {λi }i=1,2 , such that g11 = 1, g12 = 1, g21 = 0, g22 = 2. This matrix assists in transition of low frequency of trend housed in parameter vector from state at time t − 1 to t. W = diag(w1, w2) where for a smoothing coefficient 0 < β < min(λi2 )i=1,2 the expressions of w1 and w2 are: w1 = w2 =

V (1 − β )(λ1 + λ2 )(λ1 λ2 − β ) λ2 β

V (1 − β )(λ1λ2 − β )(λ1 − λ2β )(λ22 − β ) λ2 β 2

where 0 < β < 1 is a smoothing coefficient The parameters θ1 and θ2 of this model are optimally estimated using recursive equations of Harrison and Akram (1983). This second order model is the most commonly used member of the family of linear dynamic system models as in many real life cases it sufficiently represents the low frequencies of the underlying processes of many time series in a parsimonious manner. In this paper, therefore this type of model shall be referred and used for time series drifted by autoregressive (AR) noise of order p.

4.1.2 Comments In practice more specific version having eigenvalues λ1 = 1 and λ2 = 2 is preferred for a linearly growing phenomena. However, for exponential growth λ1 = 1 and λ2 < 1 are used. Exact value of λ2 that depends upon formation and the representation of growth by exponential functions, such as Logistic and Gompertz may be estimated by λ2 estimation procedure of Akram (1992).

4.2 Extended Linear Growth Model for AR(p) Drifts The observations drifted by AR(p) type noise, i.e. , Φ p (B)Et = δt may locally be modeled as: yt = f θt + Et

θt = Gθt−1 + wt Et = [Φ p (B)]−1 δt Where: B is a backward shift operator, such that BEt = Et − 1

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p Φ p (B) = ∏i=1 (1 − φi B) is invertible. That is 0 < |φi | < 1 for ∀i .

{φi }i=1,···,p are the autoregressive coefficients

δ t ∼ N(0,V ) and Wt ∼ N(0,W ) are as defined earlier. In a compact form, this conventional representation of drifted time series may be parsimoniously parameterized as: Yt = f ∗ θt∗ ∗ θt∗ = J θt−1 + wt∗ ;

wt∗ ∼ N(0,W ∗ )

Where for an AR(p) process: f ∗ = (1, 0, . . . , 0) a (1 × (n + p)) vector of known functions or constants ∗ θt∗ = (θ1∗ , . . . , θ(n+p) ) a ((n + p) × 1) vector of unknown parameters.

W ∗ = diag{(W1∗ ,W2∗ } is of rank (n + p) Where W1∗ = {Wi j }i, j=1,,p such that wi j = V for i, j = p and zero otherwise W2∗ =

diag{W1 ,W2 } V

where w1 and w2 are as defined earlier.

J = diag{Φ p , G} is a {(n + p) × (n + p)} state transition matrix of full rank Where Φ p is a (p × p) matrix of autoregressive coefficients {φi }i=1,,p defined as {φi j }i=1,,p such that

φi j = φi βφ0.5 for i = j = 1, . . . , p and zero otherwise. Where βφ , such that 0 < βφ < 1, is a damping coefficient for highly volatile noise frequencies The order and the values of {φi }i=1,,p are determined by using noise identification and testing procedure of Akram (2001). G, the state transition matrix for low frequencies of underlying processes, is as defined earlier.


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4.3 Estimation of the Parameters of the Extended Model For data Dt = (yt , Dt−1 ) assuming prior of parameter θ at time t − 1 (θt−1 , |Dt−1 ) ∼ N [mt−1 ;Ct−1 ] the posterior of θ at time t (θt , |Dt ) ∼ N [mt ;Ct ] is determined by providing initial information on f , G, W , m0 and C0 as stated by Harrison and Akram (1983) and Akram (1992) through the following recursive equations. Rt = JCt−1 J + W ∗ −1 At = Rt f ∗ V + f ∗ Rt f ∗ Ct = [I − At f ∗ ] Rt et = yt − f ∗ Jmt−1 mt = Jmt−1 + At [yt − f ∗ Jmt−1 ] where at time t, R is a system matrix, I is an identity matrix, A is an updating or gain vector, et are one step ahead forecast errors and W ∗ , a variance-covariance matrix of parameter noise, is as defined earlier. The dimensions of all these components are assumed to be compatible with their associated vectors and matrices of the recursive updating equations.

4.3.1 Example 2 For time series drifted by AR(2) noise process a linear growth model, in canonical form, at time t is operated by defining: f ∗ = ( 1 0 0 0 ) a (1 × 4) vector

θt ∗ = (θ1∗ , . . . , θ4∗ ) a (4 × 1) vector of unknown parameters. W ∗ = diag{W1∗ ,W2∗ } is a (4 × 4) matrix Where W1∗ = {wi j }i, j=1,2 such that w22 = V and zero otherwise W2∗ =

diag{w1 ,w2 } V

where w1 and w2 are as defined earlier.

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J = diag{Φ p , G} is a (4 × 4) state transition matrix of full rank Where Φ2 = {φi j }i, j=1,2 such that

φi j = φi {βφ0.5 }

i=j=1,2 and zero otherwise.

4.4 On Line Variance Learning For the above recurrence equations the observation noise variance V is assumed to be known. If unknown then at time t it may be estimated on line using the following variance estimation equations. Xt = βv Xt−1 + (1 − f ∗At )dt2 Nt = βv Nt−1 + 1, where 0 < βv < 1 is a variance damper. Vt =

Xt Nt

Ytˆ = Vt + f ∗ Rt f ∗ dt = min(et2 , ξ Ytˆ) , where ξ is a preset constant, a value of 4 for 95% confidence level and 6 for 99% confidence level. This variance learning system starts generating fairly accurate variance estimates after couple of observations.

4.5 Forecast Function For generating short, medium and long term forecasts in one go the forecast function is: (k)

Ft

= f ∗ J k mt for k ≥ 1 integers.

This function yields optimum short term forecasts and fairly accurate medium to long term forecasts at the same time.


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4.6 Comments The above model is presented for time series drifted by AR(p) noise process. In practice rarely time series drifted by more than AR(2) process are observed. In many cases, therefore linear growth model with drifted component of AR(2) is required. For more discussion see Akram (1994), Bohlin (1978) and Harrison and Akram (1983). To determine exact order of AR noise many techniques are available. For great ease however, AIC of Akaike (1973) and ATS of Akram (2001) may be employed. Among these two techniques, ATS may be effectively used by the practitioners to estimate the unknown values of autoregressive coefficients {φi }i=1,,p as demonstrated by Akram and Irfan (2007) The above model is parameterized in a canonical form. For application purpose, if desired, may be transformed to a diagonal form by using inverse transformation of Akram (1988). This model, if used in accordance with Akram (1994) is expected to take care of high frequencies of autoregressive noise while keeping low frequencies of underlying process of time series intact. As a result yielding fairly accurate forecasts.

References Akaike H (1973) Information theory and an extension of the maximum likelihood principle. In: Proceedings of the 2nd International Symposium on Inference Theory. BN Petran, F. Csáki Eds. Akadémiai Kiadi, Budapest, Hungary, pp 267–281 Akram M (1988) Recursive transformation matrices for linear dynamic system models. J Computational Stat & Data Analysis 6:119–127 Akram M (1992) Construction of state space models for time series exhibiting exponential growth. In: Computational Statistics, vol 1, Physica Verlag, Heidelberg, Germany, pp 303–308 Akram M (1994) Computational aspects of state space models for time series forecasting. Proceedings of 11th Symposium on Computational Statistics (COMPSTAT-1994), Vienna, Austria, pp 116–117 Akram M (2001) A test statistic for identification of noise processes. Pakistan Journal of Statistics 17(2):103–115 Akram M, Irfan A (2007) Identification of optimum statistical models for time series analysis and forecasting using akaike information criterion and akram test statistic: A comparative study. Proc.of World Congress of Engineers, London, vol 2, pp 956–960 Bohlin T (1978) Maximum-power validation of models without higher-order fitting. Automatica 14:137–146 Harrison P, Akram M (1983) Generalized exponentially weighted regression and parsimonious dynamic linear modelling. Time Series Analysis: Theory and Practice 3:102–139

Chapter 5

Forecast of the Traffic and Performance Evaluation of the BMT Container Terminal (Bejaia’s Harbor) D. A¨ıssani, S. Adjabi, M. Cherfaoui, T. Benkhellat and N. Medjkoune

5.1 Introduction Increasing of the traffic at the park with containers of the Bejaia harbor’s and the widening of its physical surface are not directly proportional. This is why the improvement of the productivity of the park and the good functioning of the unloading and loading system requires the specialization of the equipment and the availability of storage area which can receive the unloaded quantity, and having a configuration which will be able to adapt and answer the traffic growth. Accordingly, a first study which aimed to model the unloading process, had been realized in 2003 (Sait et al, 2007). At that time, the park with containers of the EPB (Harbor Company of Bejaia) was of 3000 ETU (Equivalent Twenty Units): 2100 ETU for the full park and 900 ETU for the empty park. The study showed that for an arrival rate of 0.55 ships/day, and a batch size of 72 ETU, the mean number of containers in the full park was of 1241 ETU. While varying the rate of the arrivals (or the batch size), the park full will be saturated for a rate of 1.0368 ships/day (or for a size of 200 ETU). This study was one of the factors that have raised awareness of the EPB to the need of creating a dedicated terminal in the treatment of container, where the birth of BMT (Bejaia Mediterranean Terminal) Company. The company began its commercial activities in July 2005. In order to ensure a good functioning of the container terminal, some performance evaluation studies are established. A first study was realized in 2007 (see Ayache et al, 2007). It had for objective the global modeling of unloading/loading process and had shown that if the number of ships (having a mean size of 170 ETU), which was of 0.83 ships/day, increases to 1.4 ships/day, the full park will undergo a saturation of 94%. Djamil A¨ıssani Laboratory LAMOS, University of Béjaia, e-mail: lamos bejaia.hotmail.com Smail Adjabi Laboratory LAMOS, University of Béjaia, e-mail: [email protected]

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D. A¨ıssani, S. Adjabi, M. Cherfaoui, T. Benkhellat and N. Medjkoune

In this work, we propose another modeling approach which consists to decompose the system into four independent sub-systems: the loading, the unloading, the full stock and the empty stock processes.

5.2 Park with Containers and Motion of the Containers In this section, we present the park with containers of BMT Company and identify the motion of the containers.

5.2.1 The BMT Park with Containers Actually, the terminal is provided with four quays of 500 m, and a park with containers which has a storage capacity of 10300 ETU. The park is divided into four zones: full park, empty park, park with refrigerating containers and a zone of discharge/potting (see Fig. 5.1.a). The park with full containers has a capacity of 8300 ETU and the one with empty containers has a capacity of 900 ETU. In addition, the BMT container terminal offers specialized installations for the refrigerating containers and the dangerous products of a capacity of 600 ETU, as well as a zone of destuffing/packing of a capacity of 500 ETU (see Fig. 5.1.a).

5.2.2 Motions of the Containers The principal motions of the containers at the Bejaia harbor’s are schematized in the Fig. 5.1.b (Ayache et al, 2007). 5.2.2.1 The Unloading Process The unloading process is made up mainly of five steps. 1. The step of anchorage: With the exception of the car-ferries and container ships, any ship arriving at the Bejaia harbor’s is put on standby in the anchorage (roads) for a duration of time which varies from a ship to another, because of the occupation of the quay stations or unavailability of pilot or tug boats. 2. The step of service: The accosting of the ships is ensured by the operational sections of the Harbor Company of Bejaia, such as the sections of piloting and towing.

5 Forecast of the Traffic and Performance Evaluation of the BMT Container Terminal

55

Fig. 5.1 (a):Plan of the terminal. (b): Plan of the model of treatment of the containers

3. Vessel handling: It consists in the unloading of the containers. That is carried out with the two gantries of quay which have carriages being able to raise the containers from the container ships, and to put them on tractors. 4. The transfer: Once the container unloaded on the tractors, it will be transported towards the zone of storage. 5. Storage: The transferred containers are arranged, piled up and stored in the park of containers. 5.2.2.2 The Loading Process The process of loading is the opposite to the process of unloading. 1. Step of anchorage: Same procedure as in the case of unloading. 2. Step of storage: The RTG (Rubber Tyre Gantry) puts the containers on the tracktors . 3. Step of transfer: The trucks transport the containers beside the container ship.

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4. Handling step: The gantry of a quay raises the container to put it on board the ship. 5. Step of service: The operational service of the EPB escorts the ship till the roads to leave the Bejaia harbor’s. 5.2.2.3 The Delivery and Restitution Processes 1. Deliveries: The delivery concerns the full containers or discharged goods. The means used to perform this operation are: RTG, trucks, stacker and forklifts if necessary. 2. Restitution of the containers: At the restitution of the containers, two zones are intended for the storage of the empty container, one for the empty containers of 20 units and the other for the empty containers of 40 units.

5.3 Mathematical Models We present in this section, the mathematical models corresponding to each system. We regarded the containers as being the customers. We impose the following assumptions: • Only one gantry in the quay for a ship. • The service duration of a truck is the sum of three variables: Duration of moving the quay till a full stock, duration of unloading of the truck by the RTG and duration of return of the truck to the quay station. • No difference between the containers. They are measured in ETU. The model of the unloading process can be represented in the diagram 5.2.a and the model of delivery process is given in the diagram 5.2.b. Remarks • The arrival of a ship represents the arrival of a containers group of a random size. • The quay is composed of two stations with size one (the queue size is limited to a random size in the sense of containers). • The treatment by the gantry is made container by container.

5.4 Calculation of the Forecasts The evolution of the number of containers handled in ETU is presented in the graph (Fig.5.3.a). It is noted that in the year 2007, BMT company treated 100000 ETU. Its objective for the year 2008 was to treat 120000 ETU. In March 2008, a calculation of forecast had been carried out. The designed series is the number of containers treated (loaded/unloaded) in ETU. The used data are


57

Fig. 5.2 (a): Diagram of the model of the unloading process. (b): Diagram of the model of the storage process.

monthly collected and are held forth over a period of two years (from January 2006 to March 2008). The method used for calculation of the forecasts is the exponential smoothing method (Blondel, 2002).

Fig. 5.3 (a): Evolution of the number of containers treated in ETU/year, (b): Original series and forecasts of the number of containers to be treated in ETU in the year 2008

The graph (Fig.5.3.b) represents the original series of the number of containers in ETU, as well as the forecasts (from April to December 2008). It is thus noted that the objective that BMT company had fixed at the beginning of the year was likely to be achieved.

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In the same situation, we completed the same work for the year 2009. The objectives of BMT company correspond to the treatment of 130254 ETU over the year. Calculations of the forecasts are presented in table 5.1. Table 5.1 Forecast of the year 2009 in ETU Month Objective of BMT Forecast of the model 1 2 3 4 5 6 7 8 9 10 11 12

10600 10730 10440 10014 10900 10750 10900 10650 10900 10570 11650 12150

10019 10468 10591 10714 10838 10962 11085 11209 11332 11456 11579 11703

Total

130254

131956

5.5 Performance Evaluation of the BMT Terminal First of all, we will carry out a statistical analysis to identify the model of network of queues which correspond to our system.

5.5.1 Statistical Analysis and Identification of Models The results of the preliminary statistical analysis (estimate and adjustment test) on the data collected for the identification of the parameters of the processes are summarized in table 5.2. According to this preliminary analysis, one concludes that the performance evaluation of the terminal of Bejaia is really a complex problem. Indeed, the system is modeled by a network of unspecified queues, because it consists of queues of type G/G/1, M [x] /G/1, with blocking,...Therefore, we cannot use analytical methods (as for the Jackson networks or BCMP) to obtain the characteristics of the system. The models are: 1. Unloading process


59

Table 5.2 Results of the statistical analysis on the collected data Process

Variable

Law

Parameters of the law

Inter-arrivals of the ships to be loaded

Exponential

1/λ = 0.000424

Size of groups to be loaded

Geometric

p = 0.0046

service duration of the gantries of quay

Normal

μ = 3.0044 and σ 2 = 1.5314062

Service duration of the trucks

Normal

μ = 6.5506 and σ 2 = 6.10435884

Inter-arrivals of the ships to be unloaded

Exponential

1/λ = 0.0005389

Size of groups to be unloaded

Geometric

p = 0.0047

Service duration of the gantries of quay

Normal

μ = 3.0044 and σ 2 = 1.5314062

Service duration of the trucks

Normal

μ = 3.0044 and σ 2 = 1.5314062

Size of groups of delivered containers/day

Uniform

Mean=121

Size of groups of restored containers/day

Uniform

Mean=126

Loading

Unloading

Storage

./G/1 ./G/m −→ .. . Arrivals −→ M [X] /./. ./G/1 −→ Departure

−→ Fig. 5.4 (a): Modeling of the unloading process 2. Loading process Arrivals of the customers of the type 1 −→ M/./.

Arrivals of the customers of the type 2 −→ D[X] /./.

./G[X] /m .. .

−→ −→

Fig. 5.4 (b): Modeling of the loading process 3. Delivery process M [X] /G[X] /1 ./G[X] /1 −→ −→ Departure Arrivals −→ Fig. 5.4 (c): Modeling of the delivery process

./G/1 | | −→ Departure | ./G/1

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4. Restitution process Arrivals of the customers of the type 1 −→ M/./.

Arrivals of the customers of the type 2 −→ D[X] /./.

/G[X] /1 −→ Departure

|

Fig. 5.4 (d): Modeling of the restitution process

In the case of the loading and restitution models, the servers will be in service only if there is at least a customer of type 1 in the first queue which will fix the size of the group to be treated. Otherwise, they will remain in a state of idleness even if there are customers of type 2 in the second queue.

5.5.2 Analytical Results Performances evaluation of systems aims to obtain the numerical values of some of their characteristics. These performances are calculated from the sample which enabled us to adjust the arrivals and services laws. The principal performances are summarized in table 3.

Table 5.3 Performances of the processes Process

Performance characteristics Mean number of ships to be loaded/day

Loading

Inter-arrival mean (day) Mean size of groups to be loaded

Value 0.6104633 1.6381 214.5278

Mean number of ships to be unloaded/day 0.7761129 Unloading Inter-arrival mean (day) Mean size of groups to unload Delivery

1.2884722 218.2174

Mean number of delivered containers/day 120.9000

Restitution Mean number of restored containers/day

125.8974

Gantry

Mean duration of service (minutes)

3.0044

Truck

Mean duration of service (minutes)

6.5506

Interpretation: According to the obtained results (table 5.3.):


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•

It is noticed that there is a mean of 0.6104633 ships which accost to the Bejaia harbor’s in order to be loaded into containers by BMT company and 0.7761129 ships for the unloading. • The ships to be loaded make a request of 214 ETU in mean and the BMT makes the unloading of 218 ETU in mean by each ship. • The mean number of delivered containers each day is n3 = 120.9000 ETU. • The mean number of restored containers each day is n4 = 125.8974 ETU. Because of the complexity of the global model, it is not possible to calculate some essential characteristics analytically. This is why we will call upon the simulation approach.

5.5.3 Simulation We designed a simulator for each model under the Matlab environment. After the validation tests of each simulator, their executions provided the results summarized in table 5.4. Table 5.4 Performances of the processes obtained by simulation Processes Performance characteristics

Loading

Mean number of loaded containers/month

4299.85

Mean number of loaded ships/month

20.0433

Mean number of ships in roads

0.0742

Mean number of ships in the quay

1.3925

Mean number of unloaded containers/month

5385.71

Mean number of unloaded ships/month

24.6808

Unloading Mean number of ships in roads

Storage

Value

0.0533


1.9308

Mean number of full containers in the park

3372.9

Mean number of empty containers in the park 211.1208

Interpretation: The results of simulation show that the total number of containers loaded during one year will be of 51598.20 ETU and the mean number of ships in roads and in the quay are respectively of 0.0742 and 1.39 ships, the total number of loaded ships during one year will be of 240.52 ships. Concerning the unloading process, the total number of containers unloaded during one year will be of 64628.52 ETU, the mean number of ships in roads and in the quay are respectively of 0.0533 and 1.9308, the total number of ships unloaded

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during one year will be of 296.17 and the total number of containers which will be handled for the year 2008 will be of 116226.72 ETU. Concerning the parks of storage, the mean number of containers in the full park will be of 3372.9 ETU and the mean number of containers in the empty park will be of 211.1208 ETU.

5.6 Variation of the Arrival Rate In order to study the behavior of the system in the case of variation of the arrival rate of the ships to be loaded and unloaded, other executions have been carried out. We have increased the number of ships at the loading and the unloading of 30%. The number of ships passes from 0.6104633 to 0.7936 per day for the loading and from 0.7761129 to 1.0089 per day for the unloading. The obtained results are summarized in table 5.5. Table 5.5 Performances of the processes in the case of increase of 30% of the number of ships arriving at the Bejaia harbor’s obtained by simulation Process

Loading

Performance characteristics

Value

Mean number of loaded containers/month

5458.30

Mean number of loaded ships/month

25.4433

Mean number of ships in roads

0.09230


1.40000

Mean number of containers unloaded /month 6958.04 Mean number of ships unloaded/month Unloading Mean number of ships in roads

Storage

31.8858 0.06690


1.90000

Mean number of full containers in the park

4874.20

Mean number of empty containers in the park 154.9814

Interpretation: With an increase of 30% of the rate of ships arriving at the Bejaia harbor’s, we note that the mean number of ships in roads and in the quay will increase a little. This means that the materials available within BMT company are sufficient to face this situation. In other words, an increase of 30% does not generate a congestion of ships in roads or in the quay. On the other hand, the mean number of handled containers will undergo a remarkable increase equivalent to 30000 ETU. This increase will not have any influence on the full stock or the empty stock. Indeed, they will pass respectively from 3372.9 ETU to 4874.2 ETU and from


63

211.1208 to 154.9814 ETU, say from 41% to 59% for the full park and from 24% to 18% for the empty park.

5.7 Conclusion The objective of this work is to analyze the functioning of the park of containers of the BMT company in order to evaluate its performances, then to foresee the behavior of the system in the case of increase of the arrivals flow of the container ships. For this, we divided the system into four independent sub-systems: the “loading”, the “unloading”, the “full stock” and the “empty stock” processes. Each system is modeled by an opened network of queues and a simulation model of the functioning of each system could be established. The goal of each simulator is to reproduce the functioning of the park with containers. The study shows that the park with containers will have the possibility of handling 116226.72 ETU, say 51598.20 ETU at loading and 64628.52 ETU at unloading and a mean number of 3372.9 ETU in the park, for entry rates of 0.6104 ships per day for the loading process and 0.7761 ships per day for the unloading process. After that, a variation of the arrivals rate of the ships was proposed with an aim of estimating its influence on the performances of the system. With an increase of 30% of the number of ships arriving at the Bejaia harbor’s, we note a small increase in the mean number of ships in roads and in the quay. On the other hand, there will be a clear increase in the total number of treated containers which will pass from 116226.72 ETU to 148996.08 ETU including 65499.6 ETU at loading and 83496.48 ETU at unloading. We also note an increase in the mean number of containers in the full park which will pass from 3372.9 to 4874.2 ETU. Regarding the number of ships, it will pass from 240.52 to 305.3 ships at loading and from 296.17 to 382.63 ships at unloading. It would be interesting to achieve this work, by discussing the following items: • An analytical resolution of the problem. • Determination of an optimal management of the machines of the BMT company. • Variation of other parameters.

References Ayache N, Hidja R, A¨ıssani D, S A (2007) Evaluation des performances du parc a` conteneurs de lentreprise bmt. rapport de recherche no. 3/2007. Tech. rep., Département Recherche Opérationnelle-Université de Béjaia. Blondel F (2002) Gestion de la production. Dunod Edition, Paris David M, Michaud JC (1983) La prévision: approche empirique dune méthode statistique,. Masson Edition, Paris

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De Werra D, Liebling TM, Heche JF (2003) Recherche Opérationnelle pour ingénieurs, Tome 2. Presses Polytechniques et Universitaires Romandes Gross D, Harris CM (1998) Fundamentals of Queuing Theory. Wiley Series in Probability and Statistics Pujolle G, Fdida S (1989) Modèles de Systèmes et de Réseaux, Tome 2,. Editions Eyrolles Ruegg A (1989) Processus Stochastiques. Presses Polytechniques et Universitaires Romandes Sait R, Zerrougui N, Adjabi S, A¨ıssani D (2007) Evaluation des performances du parc a` conteneurs de lentreprise portuaire de béjaia. In: Proceedings of an International Conference Sada07 (Applied Statistics for Development in Africa), Cotounou (Benin).

Chapter 6

A Dynamic Forecasting and Inventory Management Evaluation Approach Johannes Fichtinger, Yvan Nieto and Gerald Reiner

Abstract A common strategy for companies to hedge unpredictable demand and supply variability is to constitute safety stocks as well as safety capacity. However, classical safety stock calculations, often used in practice, assumed demand and lead time to be identical and independent distributed each, which is generally not true when considering empirical data. One cause for this problem can be the misspecification of the demand forecasting model, e. g. if a standard, additive linear regression model is used to describe heteroscedastic demand. While for a stationary demand process the amount of historical data i. e. the number of periods used for estimation of the process variability does not affect the computation, this no longer holds when using empirical data. In this study, we used a two-stage supply chain model to show that in a non-stationary setting the number of observation periods highly influence the supply chain performance in terms of on-hand inventory, fillrate and bullwhip effect. Also, we use the efficiency frontier approach to provide a single performance measure and further analyse our results.

6.1 Introduction Increasing competition leads companies in a lot of industries to pay more attention to customer satisfaction. Being able to fulfill customer orders with the “right” Johannes Fichtinger Institute for Production Management, WU Vienna – Nordbergstraße 15, A-1090 Wien e-mail: [email protected] Yvan Nieto Institut de l’entreprise, Université de Neuchâtel – Rue A.-L. Breguet 1, CH-2000 Neuchâtel e-mail: [email protected] Gerald Reiner Institut de l’entreprise, Université de Neuchâtel – Rue A.-L. Breguet 1, CH-2000 Neuchâtel e-mail: [email protected]

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Johannes Fichtinger, Yvan Nieto and Gerald Reiner

service level is crucial for customer satisfaction. Companies have to carefully adapt their delivery time to customer requirements and be prepared to cope with unplanned variation in demand as well as supply to prevent stock outs. In the context of maketo-stock manufacturing strategy, a common solution to hedge unpredictable demand and supply variability is to constitute safety stocks. This approach is widely used in practice and often relies on a classical calculation that integrates both demand and supply lead time means and standard deviations. A critical point to mention here is that the safety stock calculation assumes a stationary demand process such that the two random variables, demand and lead time, are both assumed to be identical and independent distributed each. Unfortunately, considering empirical data, demand process decomposition does not necessarily show these properties and, as a consequence, this calculation leads to volatile results. While for a stationary demand process the amount of historical data i. e. the number of periods used for estimation of the process variability does not affect the computation, this no longer holds when using empirical data. Often ignored, these points may reveal to be critical as it may impact the supply chain dynamics and lead to inappropriate inventory levels as well as service levels. The aim of this work is to present a dynamic two-stage supply chain model of a supplier and a retailer with focus on the retailer. In particular, for the retailer, we consider a periodic review inventory replenishment model, where the demand distribution is not known. Hence, the retailer uses demand forecasting techniques to estimate the demand distribution. For the supplier’s manufacturing process we assume a pure make-to-order production strategy subject to limited capacity, where orders are processed based on a strict first-in, first-out priority rule. Considering that the supply chain evaluation has to be product- and customer-specific we use an empirical reference dataset of a retail chain company to discuss our research question. We show how unstable forecast errors impact supply chain performance through its implication on order-up-to level calculation. Specifically, we build a process simulation model and measure the effect of the number of periods used in demand estimation on the performance of the supply chain. Hence, the independent variable is the number of past periods the retailer considers for calculating the mean and variance of demand. The performance measures, the dependent variables, are average on-hand inventory, the bullwhip effect as the amplification between demand variance and order variance and the fillrate as a service level criterion. Moreover, we consider the effect of manufacturing capacity (upper limit of the throughput rate) on these measures. To reduce the multi-criteria based performance measurement, we use the efficiency frontier approach to provide a single performance measure. Since our aim is to consider many aspects of a supply chain, the relevant literature is vast. Even if we use a simple inventory policy, we refer the interested reader for a comprehensive review on inventory models to Silver and Peterson (1985), Zipkin (2000) and Porteus (2002), and especially for the multi-echelon models to Axsäter (2006). The classical optimization approaches in inventory management are focusing on minimization of the total inventory system cost (Liu and Esogbue, 1999). A fundamental problem in this context is the “right” estimation of costs. This problem

6 A Dynamic Forecasting and Inventory Management Evaluation Approach

67

is mentioned also by Metters and Vargas (1999), i. e., classically, different performance measures are converted into one monetary performance measure. Therefore, these authors suggested applying data envelopment analysis to be able to take different performance measures into consideration. In general it has to be mentioned that multi-criteria optimization as well multi-objective decision making problems have been solved in many areas. Surprisingly, till now only a couple of papers have been published in the field of inventory management (see also Maity and Maiti, 2005). One of the performance measures that we consider, the bullwhip effect (Lee et al, 1997a,b; Sterman, 1989), gained significant interest of many researchers. A pointed definition of the bullwhip effect is provided by de Kok et al (2005): “The bullwhip is the metaphor for the phenomenon that variability increases as one moves up a supply chain”. Different approaches to identify the causes of the bullwhip effect have been made so far. Lee et al (1997b, 2004) describe four fundamental causes; demand signalling processing, price variations, rationing games and order batching. While the latter three are not considered in this work, the demand amplification due to the combined effects of demand signalling processing and non-zero lead times are a main focus of this work. In a work on the interface of the forecasting and replenishment system with focus on the bullwhip effect, Chen et al (2000b) use a two stage supply chain model and consider the dependencies between forecasting, lead times and information in the supply chain. In their model, the retailer does not know the distribution of demand and uses a simple moving average estimator for mean and variance of demand. Similar two-stage supply chain model have also been used by e. g. Boute et al (2007) to successfully study dynamic impact of inventory policies. The literature on the efficiency frontier approach for performance/efficiency measurement is vast after the seminal work of Charnes et al (1978). An excellent recent review can be found in Cook and Seiford (2009). Dyson et al (2001) discuss the problems of factor measurement related with percentage values, as e. g. the fillrate in our approach. The remainder of this paper is organized as follows. Section 6.2 introduces the basic supply chain model for a single supplier and a single retailer using demand forecasting. In section 6.3 we present simulation results based on numerical data and empirical examples. Section 6.5 contains further extensions to the current model and conlcluding remarks.

6.2 A Simple Supply Chain Model with Demand Forecasting Consider a simple supply chain consisting of a single retailer and a single manufacturer. The retailer does not know the true distribution of customer demand, so he uses a demand forecasting model to estimate mean and variance of demand. In each period, t, the retailer checks his inventory position and accordingly places an order, qt to the supplier. After the order is placed, the retailer faces random costumer demand, Dt , where any unfulfilled demand is lost. There is a random lead time, L,

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such that an order placed at the beginning of period t arrives at the beginning of period t + lt , where lt denotes the random realization of the order lead time placed in t. We assume that the retailer uses a simple order-up-to policy based on demand forecasting methods using regression analysis. We use aggregated weekly empirical sales data of about 220 periods (approx. 4 years) from 01/2001 to 04/2005 to estimate demand Dt for specific products. The data do not only contain sales information (units sold) but also gross price pt , stock available, number of market outlets Ot , which needs to be considered in an expanding company and a features indicator Ft (binary information to account for the effect of advertisement, e. g. by means of newspaper supplements as flyers and leaflets). To clean the data from these effects and additionally from trend and seasonality, we use a least squares regression model as proposed by Natter et al (2007). Dt = β0 + β1 pt + β2t + β3 sin

2t π 52

+ β4 cos

2t π 52

+ β5Ot + β6 Ft + et

(6.1)

Note that the sales data do not necessarily correspond to the underlying real demand process since demand during stockouts is not recorded. However, an analysis of stockout situations on the real data show that they occur in less than 2% of the selling periods. Therefore, we take the existing sales data as censored information to for demand. We tested the assumptions related with classical linear regression models for the cleaning model (see e. g. Greene, 2008, for a comprehensive discussion). There is no exact linear relationship for the independent variables in the regression (full rank assumption), and the independent variables are found to be exogenous. On the Contrary, the assumption of homoscedasticity and nonautocorrelation was not fulfilled for many products. An earlier study on the same data by Arikan et al (2007) shows that for many products a nonlinear relationship between price and demand such as (6.2) Dt = a · pt−b · et for a > 0, b > 1 could be found better explaining the pricing effect. As a consequence, for such products estimating an additive demand model as (6.1) leads to a decreasing variance of the error term, ε , in price. Hence, Var(ε |pt ) is not independent of price anymore. These in practical demand forecasting and replenishment problems inevitably occurring effects destroy the common stationarity assumption on the demand error term and, hence, are the focus of the subsequent analysis. Supplier

Retailer

Orders

x Production capacity Delivery

x Base stock policy x Target fillrate x Forecast accuracy x Observation periods

Fig. 6.1 Two stage supply chain model

Demand

Customer x Demand characteristics

Sales


69

As shown in Fig. 6.1, similar to the model of Chen et al (2000a) the retailer follows a classical infinite horizon base stock policy using weekly replenishments, where the order-up-to point St is estimated based on the expected demand for the actual period, μt , and an estimate for the standard deviation of the (1 + L) periods demand forecast error, σˆ t1+L as St = (1 + λt )μt + zt σˆt1+L ,

(6.3)

where the safety factor, zt , is chosen to meet a certain target fillrate, FR, service measure. In particular, since any unsatisfied customer demand is lost, zt is found such that it satisfies Rμt 1 − FR , (6.4) G(zt ) = · σt FR where G(·) denotes the standard normal loss function. The supply lead time the retailer faces is stochastic, where the corresponding random variable, L, has mean λt and standard deviation υt . It is well-known that for the case of fixed order costs, an (s, S) policy is optimal, however, we do not consider fixed order costs as we are interested in the effect of forecasting and the order-up-to level on the performance measures. Note that the order-up-to point in (7.1) is calculated based on the standard deviation of the (1 + λt ) period forecast error σt1+L and its estimator σˆ t1+L rather then the standard deviation of the demand over (1 + λt ) periods. As Chen et al (2000a) point out very clearly, using σˆt1+L captures the demand error uncertainty plus the uncertainty due to the fact that dt+1 must be estimated by μt+1 . Finally, defining an integer nt = max{n : n ≤ λt , n ∈ Z} helps to express the actual demand error observation, et1+L , as nt

et1+L = dt − μt + ∑ (dt+i − μt+i ) + (λt − nt ) (dt+nt +1 − μt+nt +1 ).

(6.5)

i=1

Based on the random variable of the demand error, ε 1+L , in (1 + L) periods, the estimator in period t of the standard deviation of the past demand errors can be calculated as σˆt1+L = Var(ε 1+L ) + υt2(μt λt )2 . (6.6) For the supplier’s manufacturing process we assume a pure make-to-order production strategy, where orders are processed based on a strict first-in, first-out basis. While the period length is one week for the retailer, the supplier is assumed to deliver at the end of the day the order is completely produced. We consider production of the supplier taking place on at most five days a week, hence, the supply lead time, L, can take values, l, such that 5l ∈ Z, so that l ∈ {0.2, 0, 4, 0.6, . . .}. The supplier has a fixed capacity C available solely for the retailer under consideration. For this very reason the retailer faces lead time variation, but due to missing information sharing with the supplier the retailer does not consider the supply as capacitated, and uses uncapacitated stochastic lead time models for replenishment. The lead time observation li for an order placed in i can be defined as

70


li = pi + wi ,

(6.7)

where pi = min{pi : pi qi ≥ C, 5pi ∈ Z} denotes the time necessary to complete the order qi and wi is the time during which the order was backlogged. Observe that the presented replenishment models assume the distribution of the supply lead time, L, to be independent and identical. However, due to the capacitated supplier, lead time is neither identical distributed since higher order quantities lead to stochastically longer lead times, nor is it independent due to the strict first-in first-out scheduling rule used by the supplier. The performance of the supply chain is evaluated against different measures: the ¯ the bullwhip effect as the amplification average on-hand inventory at the retailer, I, of the customer demand variance to the order demand variance, BW , and the average fillrate observed at the retailer, FR. All of these measures need to consider the available capacity at the supplier, C. While the on-hand inventory can be seen as a proxy for inventory related cost such as e. g. holding cost, the service level refers to the retailer’s “quality” of customer service, and the available capacity indicates the flexibility of the supplier within the supply chain. It is well-known from inventory theory that tradeoffs between these measures exits, e. g. the higher the average on-hand inventory, the (potentially) higher the service level and vice versa. Let xt be the quantity of goods received from the supplier at time t, then the retailer’s on-hand inventory, It , is It = max(It−1 + xt − dt , 0) for t ≥ 0,

(6.8)

and the corresponding lost sales vt are vt = − min(It−1 + xt − dt , 0) for t ≥ 0.

(6.9)

The observed average fillrate at the retailer can be calculated as FR = 1 −

T vt ∑t=1 , T D ∑t=1 t

(6.10)

and, finally, the bullwhip effect is measured as BW =

cout , cin

(6.11)

where cin and cout denote the coefficient of variation of the demand and the retailer’s order quantity , respectively (Fransoo and Wouters, 2000). Both coefficients can be easily calculated as SD(D) SD(q) , and cout = . (6.12) cin = D¯ q¯ Efficiency measurement in organizations has been the focus of numerous research activities, especially after the appearance of the seminal work of Charnes et al (1978) on the efficiency of decision making units.


71

To be able to measure the efficiency of the forecasting system and the inventory policy, we consider a set of n simulation runs j = {1 . . . n}. The performance of each run is calculated as the efficiency of the supply chain by the ratio of the weighted fillrate in per cent, FR j , to the average on-hand inventory, I¯j , uFR j . vI¯j

(6.13)

This performance/input ratio is basis for calculation of the standard engineering ratio of productivity and hence, the basis of the subsequent analysis. For our analysis, we use the extension of Banker et al (1984) of using a variable returns to scale (VRS) model such that the efficincy is defined as u FR j − u0 . v I¯j

(6.14)

Due to unknown multipliers u and v , Charnes et al (1978) and Banker et al (1984) in their extension proposed to solve the following linear programming problem. In particular, for the observation j = 0 under consideration, solve e∗0 = max u FR0 s.t. v I0 = 1 u FR j − u0 − v I j ≤ 0 j = 1, . . . , n u ≥ δ , v ≥ δ , u0 unrestricted.

(6.15)

Fig. 6.2 shows a geometrical representation of the efficiency frontier problem. By solving this input oriented model in (6.15) for each of the observations, it refers to projecting every observation to the left on the frontier. As example, in the case of the observation Obs 1, the projection is represented by the point B. The efficiency of Obs 1 is calculated as the ratio of the distances B0/A0.

6.3 Model Verification and Validation Based on our approach presented before, we will provide examples and validation for the analysis. First, we will consider artificialy generated datasets in order to validate the model against theory. Artificially generated samples were based on a normal distribution of the form N (250, 50) and used to evaluate the performance of the supply chain under 120 scenarios. Each scenario is related to a specific capacity at the supplier as well as a specific number of observation periods. Specifically, we use 5 distinct capacities, i.e. 1.1, 1.25, 1.5, 1.8 and 2.5 times the average demand of the dataset, and 24 different numbers of observation periods, i.e. each second periods starting from 4 to 50. Figure 6.3 presents the results obtained for the 3 performance measures of interests, i. e. the average on-hand inventory at the retailer, the bullwhip effect and the fillrate. It can be noticed that results are generally in


Servicelevel: Fillrate 94 95 96

97

72

B

●● ● ● ● ●● ● ● ● ● ●● ● ●

A ● Obs 1●

●

●

● ●

●

93

●

175

●

180

185 OHI

190

Fig. 6.2 Calculation of the efficiency of a single observation based on the efficiency frontier

accordance with theory. Specifically, higher capacity lead to higher performance in terms of inventory and fillrate, as benefiting from shorter lead time. Bullwhip is here neglectable, however, it illustrates, as expected from theory, that no noticable impact from the number of observation periods on the performance measures is to be reported for this stationary setting. Nevertheless, it appears that a minimum of around 18 periods of observation is necessary to permit stable estimations. A last comment is on the discrepency between the observed fillrate and the target of 98% that we assume to be related to the non-normality of the lead time. This explanation is convicing, knowing that tests involving normally distributed lead time leads to fillrate in the range of 97.2% to 98.3 (for all capacities and with sufficient number of observation periods). Bullwhip

C = 1.1

Fillrate 97.0

1.10

OHI

96.0

1.06

180

C = 1.25

20

30 40 Nr Periods

50

20

30 40 Nr Periods

50

94.0

C = 2.5

95.0

1.02

C = 1.8

0.98

160

170

C = 1.5

20

30 40 Nr Periods

50

Fig. 6.3 OHI, Bullwhip and Fillrate of a stationary demand product, plotted as a function of the number of periods used for estimating the standard deviation of the demand error term. When using around 15 periods or more, the effect of the number of periods vanishes


73

20 40 Nr Periods

C=1.8

20 40 Nr Periods

0.970 0.980 0.990 1.000

20 40 Nr Periods

C=1.5

0.970 0.980 0.990 1.000

20 40 Nr Periods

C=1.25

0.970 0.980 0.990 1.000

C=1.1

0.970 0.980 0.990 1.000

0.970 0.980 0.990 1.000

Next, we used the performance results as input for the efficiency analysis and results are presented in Fig. 6.4. It can be observed that, if any, only marginal improvements are possible by increasing the number of observation periods. Nevertheless, it is worth to mention that the optimal is proper to each capacity setting and that, for now, no comparison is possible between the different efficiency analysis. Based on the later, we consider that our model match theory expectation and is therefore verified and validated for further analysis. C=2.5

20 40 Nr Periods

Fig. 6.4 Fillrate efficiency for stationary demand products. Using 20 periods or more leads to an negligible efficiency gap smaller 1%

6.4 Empirical Data Analysis In particular, we will use empirical data presenting non stationarities to illustrate our position. We will consider two datasets, one presenting a seasonal pattern (Fig.6.4a) and a second including a single strong peak in demand (Fig.6.4b). Both datasets present therefore nonstationarities wich could have different impact on the performance of the supply chain regarding the number of observation periods considered. Simulation was performed using the same scenarios structure we presented earlier (see section 3.1) and results are presented in Fig.6.6. It can be observed that for the seasonal data , results tend to reach stability once a sufficient number of periods is available (Fig.6.6a). However, it is worth to mention that first the number of observation periods required is higher in this setting, which can be argued in the sense that, by being more structured and more volatile, valide estimations will necessitate more information, i. e. more observation. Second, fillrate remains more volatile, even for high number of observation periods and the reason for it is assumed to be linked with intrinsic dynamic of the model. In this context, order sizes are more variable, which can lead to stronger bias in lead time distribution and impact fillrate. In the case of the second dataset, interesting results in terms of performance can be observed (Fig.6.6b). In this case, the hierarchy related to capacity is much unclear considering fillrate. The number of observation periods strongly impact the service performance and make optimal setting difficult to identify.

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Product B

300

400

500

600

700

100 200 300 400 500 600 700

800

Product A

0

50

100

150

200

0

50

100

week

150

200

week

Fig. 6.5 Demand plots

Bullwhip

Fillrate

160

96.0

1.2 1.1 1.0

C = 1.5 C = 1.8

95.0

170

C = 1.25

C = 2.5

C = 1.1

210

C = 1.8

30 40 Nr Periods

50

30 40 Nr Periods

50

Fillrate

92

0.90

C = 2.5

20

93

1.05 0.95

230

C = 1.5

20

50

1.00

250

C = 1.25

30 40 Nr Periods

Bullwhip

1.10

270

OHI

20

94

50

91

30 40 Nr Periods

90

20

94.0

180

C = 1.1

97.0

190

OHI

20

30 40 Nr Periods

50

20

30 40 Nr Periods

Fig. 6.6 OHI, Bullwhip and Fillrate of non-stationary demand products A (up) and B (down)

50


75

The results from the efficiency analysis presented in Fig.6.7 confirmed the previous observations, i.e. the impact of the number of observation periods is limited in the case of the seasonal dataset (Fig.6.7a). However, the dataset including a strong peak in demand leads to erratic results regarding number of observation periods. In this last case, the highest number of periods did not lead to optimal anymore and the choice of the observation range can have strong impact on performance and this independently from the elected strategy.

0.98 0.90

20 40 Nr Periods

20 40 Nr Periods

0.98

C=2.5

20 40 Nr Periods

0.90

0.94

0.98

C=1.8

0.94 20 40 Nr Periods

C=2.5

0.94

0.98 0.90

0.94

0.98 0.94

C=1.5 0.98

20 40 Nr Periods

C=1.8

0.90

20 40 Nr Periods

20 40 Nr Periods

0.94

0.94

0.98

C=1.25

0.90

0.90

0.94

0.98

C=1.1

20 40 Nr Periods

0.90

20 40 Nr Periods

C=1.5

0.90

0.94

0.98

C=1.25

0.90

0.90

0.94

0.98

C=1.1

20 40 Nr Periods

Fig. 6.7 Fillrate efficiency for non-stationary demand products A (up) and B (down)

6.5 Conclusion We considered a dynamic two-stage supply chain model with focus on the retailer to identify the possible impact of the number of observation periods used to calculate the order-up-to level using an efficiency frontier approach. Based on this, we showed for the stationary demand case that as long as the number of periods is sufficiently large (here around 18 periods), it has no noticeable effect on the performance of the supply chain. However, considering non-stationary demand caused e. g. by a misspecification of the price dependency of demand in the demand forecasting model, the number of observation periods can lead to divergent results and considerably affect efficiency. Based on our results, we demonstrate that the impact of non stationarities when using classical safety stock calculation is highly influenced by the number of observation periods considered. In addition, as it is not possible to know ex-ante which

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periods number is optimal (neither do we know if such evaluation is possible), the danger of non stationarity should be highlighted. Here we discuss a few potential extensions to the current model. First, as mentioned in section 6.2, the retailer has no information about the cause of the lead time variability because of lacking information sharing in the supply chain. However, the benefits of information sharing for both of the supply chain partners are well-known as described in Chen (2003). In particular, in the current model, the retailer does not know about and hence, does not consider the production capacity at the supplier. On the contrary, sharing the available capacity beween the supplier and the retailer allows the retailer to apply replenishment models intergrating capacitated suppliers. We refer the interested reader to Federgruen and Zipkin (1986a,b). They showed that under certain reasonable assumptions it is optimal to follow a base-stock policy when possible and to order capacity when the prescribed quantity would exceed the capacity. By turning the problem into a cost minimization problem, cost improvements due to explicit consideration of the capacitated supplier can be evaluated. Hence, the value of information sharing in this framework becomes measureable. A second extension can be considering supplier lead time as stochastic as in Ciarallo et al (1994). They show in their model that under stochastic lead times an order-up-to policy is still optimal. Using stochastic supplier capacity, a supplier with equal mean but increasing variance in the lead time is considered less reliable. By comparing the performance measures at the retailer the value of a more reliable supplier can be made explicit. Thirdly, to fully support decision making, the efficiency frontier approch could be extended. Assuming that extra capacity has a cost, flexibility at the supplier should be integrated in the analysis to contribute to the evaluation. Also, each input could be linked to limits and weights related to the specificity of the supply chain under study in order to provide more realistic evaluation. Finally, consideration of supply chain contracts (see e. g. Cachon, 2003, for a comprehensive discussion) might help gain additional insights in the value of information sharing, the value of capacity and reliability of the supplier and the impact of the forecasting and replenishment model used by the retailer.

References Arikan E, Fichtinger J, Jammernegg W (2007) Evaluation and extension of single period combined inventory and pricing models. In: Proceedings of the 14th International Annual EurOMA Conference, Ankara, Turkey Axsäter S (2006) Inventory Control. Springer Verlag Banker RD, Charnes A, Cooper WW (1984) Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science 30(9):1078 – 1092 Boute RN, Disney SM, Lambrecht MR, Van Houdt B (2007) An integrated production and inventory model to dampen upstream demand variability in the supply


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chain. European Journal of Operational Research 178(1):121–142 Cachon GP (2003) Supply chain coordination with contracts. In: de Kok A, Graves S (eds) Supply Chain Management: Design, Coordination and Operation, Handbooks in Operations Research and Management Science, vol 11, pp 227–339 Charnes A, Cooper W, Rhodes E (1978) Measuring the efficiency of decision making units. European Journal of Operational Research 2(6):429–444 Chen F (2003) Information sharing and supply chain coordination. In: de Kok T, Graves S (eds) Supply Chain Management: Design, Coordination, and Operation, Handbooks in Operations Research and Management Science, vol 11, Elsevier Chen F, Ryan J, Simchi-Levi D (2000a) The impact of exponential smoothing forecasts on the bullwhip effect. Naval Research Logistics 47(4):271–286 Chen YF, Drezner Z, Ryan JK, Simchi-Levi D (2000b) Quantifying the bullwhip effect in a simple supply chain: The impact of forecasting, lead times, and information. Management Science 46(3):436–443 Ciarallo F, Akella R, Morton T (1994) A periodic review, production planning model with uncertain capacity and uncertain demand-optimality of extended myopic policies. Management Science 40(3):320–332 Cook WD, Seiford LM (2009) Data envelopment analysis (DEA) - thirty years on. European Journal of Operational Research 192(1):1–17 de Kok T, Janssen F, van Doremalen J, van Wachem E, Clerkx M, Peeters W (2005) Philips electronics synchronizes its supply chain to end the bullwhip effect. Interfaces 35(1):37–48 Dyson RG, Allen R, Camanho AS, Podinovski VV, Sarrico CS, Shale EA (2001) Pitfalls and protocols in dea. European Journal of Operational Research 132(2):245–259 Federgruen A, Zipkin P (1986a) An inventory model with limited production capacity and uncertain demands I. the average-cost criterion. Mathematics of Operations Research 11(2):193–207 Federgruen A, Zipkin P (1986b) An inventory model with limited production capacity and uncertain demands II. the discounted-cost criterion. Mathematics of Operations Research 11(2):208–215 Fransoo JC, Wouters MJ (2000) Measuring the bullwhip effect in the supply chain. Supply Chain Management: An International Journal 5(2):78–89 Greene WH (2008) Econometric Analysis, 6th edn. Pearson Prentice Hall, Upper Saddle River, New Jersey, US Lee HL, Padmanabhan V, Whang S (1997a) The bullwhip effect in supply chains. Sloan management review 38(3):93–102 Lee HL, Padmanabhan V, Whang S (1997b) Information distortion in a supply chain: The bullwhip effect. Management Science 43(4):543–558 Lee HL, Padmanabhan V, Whang S (2004) Comments on information distortion in a supply chain: The bullwhip effect. Management Science 50(12):1887–1893 Liu B, Esogbue A (1999) Decision criteria and optimal inventory processes. Kluwer Academic Publishers

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Maity K, Maiti M (2005) Numerical approach of multi-objective optimal control problem in imprecise environment. Fuzzy Optimization and Decision Making 4(4):313–330 Metters R, Vargas V (1999) A comparison of production scheduling policies on costs, service level, and schedule changes. Production and Operations Management 8(1):76–91 Natter M, Reutterer T, Mild A, Taudes A (2007) Practice prize report – an assortment-wide decision-support system for dynamic pricing and promotion planning in DIY retailing. Marketing Science 26(4):576–583 Porteus EL (2002) Foundations of Stochastic Inventory Theory. Stanford University Press Silver E, Peterson R (1985) Decision systems for inventory management and production planning. Wiley, New York et al. Sterman JD (1989) Modeling managerial behavior: Misperceptions of feedback in a dynamic decision making experiment. Management Science 35(3):321–339 Zipkin PH (2000) Foundations of Inventory Management. Shelstad, Jeffrey J.

Chapter 7

Performance Evaluation of Process Strategies Focussing on Lead Time Reduction Illustrated with an Existing Polymer Supply Chain Dominik Gläßer, Yvan Nieto and Gerald Reiner

Abstract The ability to fulfil customer orders is crucial for companies which have to operate in agile supply chains. They have to be prepared to respond to changing demand without jeopardizing service level, i. e. delivery performance is the market winner (Christopher and Towill, 2000; Lee, 2002). In this context, lead time reduction (average as well as variability) is of key interest since it allows increasing responsiveness without enlarging inventories. In front of these possible levers (e. g. Chandra and Kumar (2000), the question arises of the dynamic assessment of potential process improvements for a specific supply chain and moreover a combination of potential process improvements related to an overall strategy (responsive, agile, etc.). Using process simulation, we demonstrate how the coordinated application of strategic supply chain methods improves performance measures of both intra- (lead time) and interorganizational (service level) targets.

7.1 Introduction The intention of this study is to analyse and assess the effects of shortening lead time, i. e., average as well as variability, on the performance of the entire supply chain (delivery service, delivery time, cost, etc.). There are a great number of different strategic/tactical supply chain approaches (Chandra and Kumar, 2000; Mentzer Dominik Gläßer Institut de l’entreprise, Université de Neuchâtel – Rue A.-L. Breguet 1, CH-2000 Neuchâtel e-mail: [email protected] Yvan Nieto Institut de l’entreprise, Université de Neuchâtel – Rue A.-L. Breguet 1, CH-2000 Neuchâtel e-mail: [email protected] Gerald Reiner Institut de l’entreprise, Université de Neuchâtel – Rue A.-L. Breguet 1, CH-2000 Neuchâtel e-mail: [email protected]

79

80

Dominik Gläßer, Yvan Nieto and Gerald Reiner

et al, 2001) that make it possible to improve the supply chain processes by means of, e. g., demand forecast (see Winklhofer et al (1996) for a review), capacity management, organizational relations, better communication, reduction of supply chain echelons and adapted inventory management. Also, the possibility of moving the customer order decoupling point has been recognized (Olhager, 2003), opening the door to postponement strategies, etc.. In front of these possible levers, the question arises of the dynamic assessment of potential process improvements for a specific supply chain and moreover a combination of potential process improvements related to an overall strategy. Supply chain evaluation is of primarily importance in order to support decision making. We will demonstrate that these theoretical concepts as well as the related restrictions have to be modified under consideration of “real” processes. Therefore, the question arises if these concepts are robust enough to improve also “real” processes. The investigations will be carried out on the basis of quantitative models using empirical data (Bertrand and Fransoo, 2009). Basically, with the quantitative examination of empirical data a model will be developed which reproduces causal correlations between the control variables and the performance variables. Furthermore, Bertrand and Fransoo (2002) pointed out that this methodology offers a great opportunity to further advance the theory. According to Davis et al (2007) the choice of simulation technology is an important decision when it comes to achieving the research objective. Thus, simulation models will be developed, e. g., discrete event simulation (Sanchez et al, 1996), since the possibility of understanding the supply chain as a whole and analyzing and assessing different strategic/tactical action alternatives offer a considerable benefit. This is why we have opted to use ARENA for developing the simulations models (Kelton et al, 2003). First, Section 2 discusses the effects of optimised lead time as regards supply chain performance. Furthermore, the importance of supply chain evaluation is emphasised. Then, in Section 3, we set out our research approach with the help of a polymer processing supply chain. Finally, Section 4 provides concluding remarks plus a look at other research possibilities.

7.2 Theoretical Background Cutting lead time is understood by experienced managers but is seldom awarded sufficient importance. Thus, it is that Little’s Law (Hopp and Spearman, 1996) says that cutting delivery time also cuts work in process. However, strategic advantages such as improving service level or cost advantages, can also be achieved. If one considers the classic formula for calculating the safety stock that is used as part of a reorder point replenishment policy, (7.1) Is = z μτ υ 2 + λτ στ2 it is evident that delivery time directly affects this (Silver et al, 1998). Here, μτ stands for the delivery time mean and στ2 for the delivery time variance. The other

7 Performance Evaluation of Process Strategies Focussing on Lead Time Reduction

81

parameters stand for demand mean (λτ ) and demand variance (υ 2 ) as well as the safety factor z, which represents a trade-off between service level and stock keeping costs, and Is for safety stock. Therefore there is a lot of interest in reducing the variance as well as average delivery time. On the one hand, this result in reduced safety stock that is reflected by lower stock keeping costs. On the other hand, this in no way worsens the service level, e. g. the number of stock outs. Thus the operational objective of a supply chain, i. e. increased customer satisfaction and lower costs at the same time, becomes more realistic. This can even turn out to be a strategic competitive advantage. A decisive element is the customer order decoupling point (CODP) (Mason-Jones et al, 2000). It is the point where the forecast-driven standard production, mostly serial production of standard components (PUSH), and the demanddriven production, i. e. commissioned production in response to customer orders or other requirement indicators (PULL) meet. Physically, the decoupling point in the supply chain is the ultimate inventory where components not yet relating to any order (Mason-Jones and Towill, 1999). The further downstream in the supply chain the decoupling point is, the less the quantities taken from the inventories agree with real demand at the point of sale (POS). Owing to the fact that most supply chain partners do not see real customer demand, they tend to be forecast-driven and not demanddriven (Christopher and Towill, 2000), which also enforces the so-called “bullwhip effect” (increasing fluctuations in order quantities and inventory up-stream in the supply chain whilst end customer demand remains constant (Lee et al, 2004)). To increase competitive advantage, Olhager (2003) determines that companies can either keep the CODP at its current position and reduce delivery lead time or maintain the delivery lead time and move the CODP upstream in order to reduce or clear stocks. Strategically positioning the CODP particularly depends on the production to delivery lead time (P/D) ratio and on relative demand volatility (RDV) (standard deviation of demand relative to the average demand). In this way, for example, a make to order (MTO) strategy can only be achieved if the P/D ratio is less than 1 (Olhager, 2003). This is because when production lead time is greater than the delivery lead time of a customer order, customer service of course suffers (Jammernegg and Reiner, 2007). On the other hand, it is not advisable to apply a make to stock (MTS) strategy (lead time is zero) if the RDV is very high because this results in huge inventories if customer service is to be maintained, and this of course results in high inventory costs. If, in this case, the P/D ratio is greater than 1, then some components would have to be produced for stock, which leads to an assembly to order (ATO) or an MTS strategy. The importance of lead time is also emphasised by Cachon and Fisher (2000), in that they assert that reducing lead time or batch size can affect supply chain performance more than information sharing. Likewise, in the 12 Mason-Jones et al (2000) for simplifying material flow cutting lead time is an important point.

82


7.2.1 Supply Chain Evaluation Evaluation of real supply chain processes is always challenging since a valid estimation can only be obtained through a detailed, specific process analysis. Improvements of a specific supply chain process can never be 100% applied (copied) to another setting. Nevertheless, they can be used as best practice indicating improvement potentials to another company / supply chain. This analysis must be product-specific as well as company-specific and the performance measures have to be selected carefully and in accordance with the specificity of the system under study (Reiner and Trcka, 2004). An important step in defining suitable performance measures is determining market qualifiers and market winners, which determine the alignment and therefore different metrics for leanness and agility of supply chain performance (Mason-Jones et al, 2000; Naylor et al, 1999). When drawing up the analysis and assessment model a product-specific supply chain design method should be selected in order to achieve results that are close to reality. This method provides for the fact that a supply chain always has to be designed in a product-specific and customerspecific way (Fisher, 1997) and that the alignment of the supply chain with regard to its leanness, agility or a combination of both (Lee 2002, Christopher and Towill 2000) plays a decisive role. If a supply chain already exists in reality, then the necessary data for the specified performance measures can be obtained by i. e. analysing existing IT systems as well as interviewing the supply chain partners. However, if alternative supply chain strategies have to be analysed in terms of their performance, then data is never available. In this case, missing values can be calculated, estimated or obtained by simulation. But calculation is often impossible and a general estimation is too imprecise (Jammernegg and Reiner, 2007). Dynamic stochastic computer simulations can provide not only average values for performance measures but also give information about their probabilistic distribution (Kelton et al, 2003) because of the use of random variables (Jammernegg and Reiner, 2007). Random variables, which simulate risks, are essential to reliable evaluations because, according to Hopp and Spearman (1996), risks negatively affect supply chain performance. To enable precise evaluation, the model must include all important process-related matters.

7.3 Illustration of the Supply Chain To illustrate the ”real” improvement potential of theoretical lead time reduction approaches, we analysed empirical data from a supply chain in the polymer as well as furniture industry. The supply chain is characterized by three levels, i. e. a supplier, a manufacturer and a sales office, and ends with a market-leading OEM as unique customer. In this case, delivery performance is the market winner and on-time delivery is therefore crucial to maintain customer loyalty. Due to the tremendous variety of products offered by the manufacturer (more than 50000), the analysis had to be limited to key articles. The selection of the product was performed using ABC-XYZ


83

analysis. This classification is an extension of the ABC analysis (Vollmann et al, 2004), because it not only takes the value into consideration, but also the variability of the demand (Schönsleben, 2004). We opt for the most sold product, which has a coefficient of variation (standard deviation/mean) greater than 2/3. Thereby, this product represents the AY category (Reiner and Trcka, 2004).

7.3.1 Process Design The manufacturer, located in Western Europe, delivers goods to a sales office located in Eastern Europe. In turn, the sales office supplies the four OEM production plants (C1, , C4) belonging to the customer and also located in the eastern part of Europe. The entire procedure is set out in Fig. 1, with the sales office as well as the production sites arranged as in reality. In more details, the sales office uses its inventory to fulfil the customer orders. As soon as the inventory level at the sales office decreases down to a reorder point a stock replenishment order is placed at the manufacturer. The manufacturer must then supply the goods and send them to the sales office as fast as possible. No delivery time is specified. It is to be borne in mind that the manufacturer’s finished goods inventory merely serves as a buffer store for transport purposes (batching) and is thus not able to deal with any significant demand fluctuations because the manufacturing strategy is make to order for the manufacturer.

WLR WD RU U VS GH DQ 2U 7U Q

Fig. 7.1 The initial process

The sales distribution process is to be regarded as based on the classic push principle (make to stock). In a dynamic environment where there is uncertainty about demand and fluctuations in demand this make to stock strategy may lead to great

84


problems. Fig. 2 shows the stock movements at the sales office over a year. The diagram shows that there is an increase of stock outs during the first half of the year, and this has a negative effect on customer satisfaction. The problems associated with in this setting are manifold. (1) Owing to the irregular pattern of customer order placing, it is difficult for the sales office to produce a forecast for the future. (2) Furthermore, available information of the sales office is not sent promptly to the manufacturer. (3) There is a lack of transparency, the manufacturer is not aware of actual customer demand. Therefore, he is not able to discern whether or not there is a genuine customer order behind the stock replenishment order placed by the sales office. This frequently leads to unfavourable prioritisation of the production orders and this, in turn, sometimes results in long and varying delivery periods. (4) There is no classical replenishment policy used by the sales office, so that decisions concerning reorder points and order quantity are mostly made on a one-off basis by the sales office staff. 6WRFN0RYHPHQW

4XDQWLW\

'D\V

Fig. 7.2 Stock movements at the sales office

As already mentioned, when choosing performance measures, a special focus is on the total lead time as well as on costs and customer satisfaction (number of stock outs). The period between receipt of the order at the manufacturer’s sales office and the point when the goods are dispatched to the customer from the sales office inventory is described as the total lead time. Reducing lead time has financial implications as well as strategic effects (Gunasekaran et al, 2001). Table 1 sets out initial situation performance measures. Long lead times and large numbers of stock outs are particularly apparent. Stock keeping costs are correspondingly low owing to the many stock outs. In the following the representation of the initial situation based on actual historical data is called initial scenario.

7.3.2 A Simulation Study For our simulation model, we use discrete event simulation (ARENA). We apply the model to asses the performance of different supply chain settings as well as to


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evaluate design alternatives. For each scenarios tested, replications were carried out in order to asses the variability and the robustness provided by each strategy (Reiner and Trcka, 2004). One simulation run is for a period of 365 days. Quantitative models based on empirical data are largely dependent on the data they integrate as well as on process design descriptions. These are necessary for making sure that the way the model works comes as close as possible to actual observations and processes. In order to obtain a coherent data base free of organisational barriers, the data triangulation approach was chosen (Croom, 2009). In particular, we looked at the existing IT systems at the plant, the sales office and the organisational administration departments. Based on direct data access we ensured that data could be directly acquired from the source using the database query. The model design was adapted in line with the product-specific supply chain method based on analyses and observations of reality, e. g. participant observations and questioning responsible supply chain managers. Product specification, according to Mason-Jones et al (2000), yielded that the market winner is the level of readiness to deliver, whereas quality, costs and lead time are the market qualifiers. This indicates an agile supply chain environment. For model validation, the initial scenario was simulated and the result data were compared with the real data. The comparison showed that the results of the model reflect the reality. Finally the completed model design including the simulation results were again confirmed through responsible supply chain managers and participant observations.

7.3.3 Scenario 1 - Forecast Based Inventory Management Based on interviews we figured out that a 4-week rolling forecast from customer could be provided, which will constitute the core alternative of our first scenario. The rolling forecast represents actual order entry with optional manual adoptions from the customer. In addition, and in order to support the impact of the forecast, an (s,S) inventory policy will be applied at the sales office, with a safety stock calculated as in eq. 1 with a target cycle service level of 95%. The order quantity also takes the manufacturer’s batch size into account. All applied distributions for stochastic input variables (e. g. delivery time between manufacturer and sales offices incl. production time, transport cost) were worked out on the basis of real data, taking account of chi-square and Kolmogorov-Smirnov goodness-of-fit hypothesis tests. In addition, all distributions have been validated in a graphical evaluation. As it has not yet been possible to estimate the precision of the customer’s forecast, it was assumed in the simulation that the actual order can deviate 20% from the forecast per period. The results of the scenario 1 are presented in Table 1.

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7.3.4 Scenario 2 - Improvements Along the Supply Chain Scenario 2 focuses on shortening the supply chain by closing the inventory at the sales office and by direct customer delivery from the manufacturer. Now, the manufacturer’s order policy envisages always having sufficient articles in stock for the next two weeks (based on average demand per week). Therefore, in order to enable this strategy, a forecast is necessary and the 4-weeks rolling forecast from scenario 1 was conserved. By doing so, the manufacturer becomes aware of the actual customer requirement leading to an upstream move of the CODP. It is worth to mention that the sales office stays responsible for customer relation, contract extension and contract monitoring. In addition, this strategy results in new transport costs. New transport prices were estimated from interviews with the carrier and were factored into the simulation. Fig. 3 shows the entire process.

& 5

&5 0

0

Fig. 7.3 Improved process of scenario 2

7.3.5 Simulation Results The performance measures are set out in Table 21.2 and are related to an entire year. Based on the described improvements in scenario 1, we are able to reduce the number of stock outs, which is a direct indicator of customer satisfaction. Lead times and costs can not be reduced. Owing to the delivery time (mean and the variance) between sales office and manufacturer, it is necessary to keep large stocks, which in turn has a negative effect on stock keeping costs and the profit margin. This case


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would also mean building work to extend the sales office inventory to handle the high stock of inventory. As it is not possible to find an improved solution according to all of our performance dimensions (lead time, customer satisfaction and cost), we decided to consider the entire supply chain in scenario 2. By cutting the flow of products through shortening the supply chain and postponing the CODP, it was possible to achieve a marked reduction in total lead time in scenario 2. Compared to the initial scenario, these activities also had a positive effect on customer satisfaction because it is possible to react much faster to customer requirements. Also stock keeping costs are reduced as sales office stores are no longer required and production is carried out on forecasts provided by the customer. In order to be complete, it has to be mentioned that this strategy would only be possible by extending the manufacturer inventory capacity. Nevertheless, we assume that this would be a realistic investment as the costs of building an extension to the manufacturer’s stores would easily be compensate by the saving on the transport costs side within one year.

7.4 Conclusion In this paper we analysed and assessed two different possibilities for supply chain improvements. We regarded their effects on lead time and it was possible to show financial and strategic enhancements. Our approach was illustrated by a polymer supply chain with a major OEM as end customer. For each of the alternatives, the performance was measured using lead time, finished articles inventory stocks as well as costs, number of stock outs and transport costs; where the number of stock outs constitutes a decisive index for customer satisfaction. The threshold number of stock outs should be less than 10 days per year. We were able to confirm the positive impact of lead time reduction on supply chain performance, i. e. the simultaneous reduction of inventory and increase of customer satisfaction. We managed to identify this specific dynamic behaviour by quantifying the benefits earned through each alternative. Further on, we confirmed the importance of considering the supply chain as a whole when assessing improvement alternatives. Our results demonstrate that the benefits of certain alternatives can only be realised if improvements are aligned along the supply chain partners, e. g. inventory management is based on the customer forecast and linked to the production planning. We believe these results to be interesting for both academics and practitioner as they contribute to better understanding the dynamics of the supply chain and the importance of the entire supply chain-specific evaluation of improvements. One of our next research activities will be to implement the most suitable alternative, in order to be able to draw further conclusions about the model (see also Mitroff et al (1974) and to ascertain an appropriate forecast algorithm based on historical data to support the customer forecast.

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Table 7.1 Results of initial scenario and simulation runs Initial scenario Scenario 1 1 Total lead time (order entry at 43,14 manufacturer up to delivery of goods at the sales office in days)

Scenario 2

54,31 min 7,67 max 112,67 σ 16,60

14,62 min 2,68 max 38,67 σ 4,02

20,28 min 0.0 max 48,80 σ 7,47

12,93 min 0.0 max 38,67 σ 7,14

3 Delivery time between sales 35,44 office and manufacturer in days

35,11 min 1 max 79 σ 14,93

Omitted min 1 max 87,44 σ 14,35

4 Production lead time in days

No detailed consideration. Included in row 3

No detailed consideration. Included in row 3

1,73 min 0.82 max 11.1 σ 1.4

5 Stock outs in days

57

0,76 min 0.0 max 6 σ 1.5

1,75 min 0.0 max 6,04 σ 2.55

6 Transportation costs manufacturer → sales office in Euros

150000

158964 min 150800 max 163800

Omitted

7 Transportation costs sales office → customer 1-4 in Euros

33000

31895 min 29300 max 34430

Omitted

8 Transportation costs manufacturer → customer 1-4 in Euros

Omitted

Omitted

119600 min 113100 max 126100

9 Inventory costs sales office in Euros

7091

18753 min 9964 max 21779

Omitted

10 Inventory costs manufacturer in Euros

1774

1818 min 1778 max 1883

8904 min 7686 max 9196

2 Period of storage at the sales office (scenario 1) respectively the manufacturer (scenario 2) in days

7,8

Acknowledgements Partial funding for this research has been provided by the project “Matching supply and demand – an integrated dynamic analysis of supply chain flexibility enablers” supported by the Swiss National Science Foundation.


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References Bertrand J, Fransoo J (2002) Operations management research methodologies using quantitative modeling. International Journal of Operations and Production Management 22(2):241–264 Bertrand J, Fransoo J (2009) Researching Operations Management, 1st edn, Routledge, New York, chap Modelling and Simulation Cachon GP, Fisher ML (2000) Supply Chain Inventory Management and the Value of Shared Information. Management Science 46(8):1032–1048 Chandra C, Kumar S (2000) Supply chain management in theory and practice: A passing fad or a fundamental change? Industrial Management and Data Systems 100(3):100–13 Christopher M, Towill D (2000) Supply chain migration from lean and functional to agile and customised. Supply Chain Management: An International Journal 5(4):206–13 Croom S (2009) Researching Operations Management. 1st edn, Routledge, New York, chap Introduction to Research Methodology in Operations Management Davis J, Eisenhardt K, Bingham C (2007) Developing theory through simulation methods. The Academy of Management Review (AMR) 32(2):480–499 Fisher M (1997) What is the right supply chain for your product? A simple framework can help you figure out the answer. Harvard Bus Rev 75(2):105–116 Gunasekaran A, Patel C, Tirtiroglu E (2001) Performance measures and metrics in a supply chain environment. International Journal of Operations and Production Management 21(1/2):71–87 Hopp WJ, Spearman ML (1996) Factory Physics: Foundations of Manufacturing Management. Irvin Inc., Chicago Jammernegg W, Reiner G (2007) Performance improvement of supply chain processes by coordinated inventory and capacity management. International Journal of Production Economics 108(1-2):183–190 Kelton W, Sadowski R, Sturrock D (2003) Simulation with ARENA, 3rd edn. McGraw-Hill Science/Engineering/Math Lee H (2002) Aligning supply chain strategies with product uncertainties. California Management Review 44(3):105–119 Lee HL, Padmanabhan V, Whang S (2004) Comments on Information Distortion in a Supply Chain: The Bullwhip Effect. Management Science 50(12):1887–1893 Mason-Jones R, Towill D (1999) Using the information decoupling point to improve supply chain performance. International Journal of Logistics Management 10(2):13–26 Mason-Jones R, Naylor B, Towill D (2000) Lean, agile or leagile? Matching your supply chain to the marketplace. International Journal of Production Research 38(17):4061–4070 Mentzer J, DeWitt W, Keebler J, Min S, Nix N, Smith C, Zacharia Z (2001) Defining supply chain management. Journal of Business logistics 22(2):1–26

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Mitroff I, Betz F, Pondy L, Sagasti F (1974) On managing science in the systems age: Two schemas for the study of science as a whole systems phenomenon. Interfaces 4(3):46–58 Naylor J, Naim M, Berry D (1999) Leagility: Integrating the lean and agile manufacturing paradigms in the total supply chain. International Journal of Production Economics 62(1-2):107–118 Olhager J (2003) Strategic positioning of the order penetration point. International Journal of Production Economics 85(3):319–329 Reiner G, Trcka M (2004) Customized supply chain design: Problems and alternatives for a production company in the food industry. A simulation based analysis. International Journal of Production Economics 89(2):217–229 Sanchez S, Sanchez P, Ramberg J, Moeeni F (1996) Effective engineering design through simulation. International transactions in Operational research 3(2):169– 185 Schönsleben P (2004) Integral logistics management: Planning & control of comprehensive supply chains. CRC Press Silver E, Pyke D, Peterson R (1998) Inventory management and production planning and scheduling, 3rd edn. Wiley New York Vollmann T, Berry W, Whybark D, Jacobs F (2004) Manufacturing planning and control systems for supply chain management, 5th edn. McGraw-Hill Winklhofer H, Diamantopoulos A, Witt S (1996) Forecasting practice: A review of the empirical literature and an agenda for future research. International Journal of Forecasting 12(2):193–221

Chapter 8

A Framework for Economic and Environmental Sustainability and Resilience of Supply Chains Heidrun Rosiˇc, Gerhard Bauer and Werner Jammernegg

Abstract Traditionally supply chain management decisions are based on the economic performance which is expressed by financial and non-financial measures, i.e. costs and customer service. From this perspective, in the last decades, several logistics trends, i.e. outsourcing, offshoring and centralization, emerged. Recently, studies have shown that the focus on the cost aspect is no longer sufficient. Due to internal and external drivers (e.g. customer pressure, regulations, etc.) environmental criteria become more and more important for the decision-making of individual enterprises. Furthermore, the risk which is related to the increased transportation distances resulting from these strategies is often not taken into account or underestimated. These shifts in priorities of companies force them to search for new logistics strategies that are at the same time cost-efficient, environmentally friendly and reliable. Based on this integrated perspective new logistics trends, like on- and nearshoring, flexible supply base or flexible transportation, have come up recently and will gain more importance in the near future. Relying on a flexible supply base a company can benefit from low costs in an offshore facility and simultaneously be able to respond quickly to demand fluctuations and react to delivery delays and disruptions by serving the market also from an onshore site. A single-period dual sourcing model is presented to show the effects of emission costs on the offshore, onshore and total order quantity.

Heidrun Rosiˇc Vienna University of Economics and Business, Nordbergstraße 15, 1090 Vienna, Austria, e-mail: [email protected] Gerhard Bauer Vienna University of Economics and Business, Nordbergstraße 15, 1090 Vienna, Austria, e-mail: [email protected] Werner Jammernegg Vienna University of Economics and Business, Nordbergstraße 15, 1090 Vienna, Austria, e-mail: [email protected]

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Heidrun Rosiˇc, Gerhard Bauer and Werner Jammernegg

8.1 Introduction Traditionally supply chain management decisions are based on the economic performance which is expressed by financial and non-financial measures, i.e. costs and customer service. From this perspective, in the last decades, different logistics trends, i.e. outsourcing, offshoring and centralization, have emerged. Even though these trends seem to be rather “old” they are still prevailing in today’s businesses. Recently, a study conducted in Austria has shown that 41% of the interviewed companies still intend to offshore some of their production activities in the following two years. Furthermore, 35.4% of them plan to move their production sites to Asia; especially China is a prominent destination for offshoring. The low cost of the production factors (personal, material, etc.) are the key drivers for their decisions (Breinbauer et al, 2008). A European-wide study carried out by Fraunhofer ISI concerning offshoring showed similar results. Between 25% and 50% of the surveyed enterprises moved parts of their production abroad in the years 2002 and 2003 (Dachs et al, 2006). Further examples can be found. For instance, the Austria-based Knill Group, which is active in the field of infrastructure, supplying systems and applications for energy and data transmission, built new production facilities in India and China within the past 36 months in order to take advantage of lower wages in Asia (Breinbauer et al, 2008). NXP, a leading semiconductor company is headquartered in Europe and employs more than 33,500 employees. The company pursued a strong offshoring strategy and now more than 60% of its production activities are located in Asia, 5% in America; only 33% have remained in Europe. Also, AT&S, a large Austrian manufacturer of printed circuit boards, continues its offshoring strategy. In January 1999, AT&S started operating in India by acquiring the largest Indian printed circuit board manufacturer and now it will build a second facility located nearby. The investments for this project will amount to 37 million Euros and production activities shall start in the third quarter of 2009. Besides, AT&S operates facilities in China and Korea. In section 2 prevalent logistics trends are presented focusing on a cost perspective, thereby showing the trade-offs that exist between the different cost components. The trends presented, i.e. outsourcing, offshoring and centralization, usually lead to lower production (procurement) costs in the case of offshoring and outsourcing or lower inventory costs in the case of physical centralization. But, in general, they result in an increase of transportation distances, therefore making supply chains longer and/or more complex. Often in the evaluation of these strategies side effects of increased transportation distances are not taken into account adequately. Therefore, in section 3 in addition to the economic criteria, “soft” factors, like lead time, delivery reliability, flexibility, etc. and the environmental impact are included. Based on this integrated perspective consisting of costs, risks and environment new logistics trends are highlighted. One of these new logistics trends is then analyzed in more detail, namely flexible supply base with the specific variant dual sourcing. In section 4 a transport-focused framework for dual sourcing (off- and onshore supply source)

8 A Framework for Economic and Environmental Sustainability and Resilience of SC

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and in section 5 a single-period model for dual sourcing including emission costs are presented.

8.2 Prevalent Logistics Trends: Cost Perspective The subject of supply chain management is the organization of the transformation of raw materials into final products by a well defined network of manufacturing, warehousing and transportation processes. Most of the necessary activities are determined by the design of the supply chain. In network design, for instance, it is decided where manufacturing activities take place, which location performs a certain activity, where procurement and/or distribution centers are located and how the transportation is handled between the different stages. Traditionally, these decisions are based on the economic performance which is expressed by financial and non-financial measures, i.e. costs and customer service. Often these measures are conflicting, like optimizing the total landed cost of all involved transformation processes and satisfying customer requirements. A first trade-off is between logistics cost and customer service: high levels of product availability can be achieved with high inventory and thus high inventory cost; short delivery times are possible with additional resources for manufacturing and/or transportation related with an increase of the respective cost. Moreover, a second trade-off must consider the costs of resources (manufacturing, transportation, storage facilities). In order to stay competitive in the market, an enterprise chooses the strategy which is most efficient, generates lowest total landed cost (facilities, inventory and transportation) and satisfies customer requirements. Different trends, i.e. outsourcing and offshoring of production activities and physical centralization, have emerged due to a focus on cost reduction. Outsourcing of production activities means to subcontract a process to a third-party in order to concentrate investments and time on the core competencies of a company. Outsourced processes may be done more efficiently and cheaper by a third party which gains economies of scale. Further, the fixed cost of production can be reduced (Chopra and Meindl, 2006). Offshoring is defined as locating activities abroad with varying degree of the geographical distance between the original and the new location depending on the author, e.g., “outside a country’s boundaries”, “outside the first world”, “outside of the continent”. In this paper, offshoring does not include each transfer of manufacturing facilities outside a country’s boundaries, but the term offshoring only applies to those relocations made to a far-distant country. With respect to the term “far-distant country” it has to be kept in mind that the actual geographical distance is relevant and not the legal boundaries of a country. The main driver for offshoring is to lower operational costs due to lower wages of the workforce abroad or lower raw material costs. Further reasons for offshoring are gaining market access, following a key customer or productivity increases. Typical offshore regions are situated in Asia because there a company can take advantage of significantly lower labor costs. The dislocation of production activities from West-

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ern Europe to Eastern Europe is often called nearshoring as the distance and the cultural differences are less (Ferreira and Prokopets, 2009). Physical centralization means that the number of production, procurement and/or distribution sites is reduced to a single one, this means “consolidating operations in a single location” (Van Mieghem, 2008). The main goal of centralization is to pool risk, reduce inventory and exploit economies of scale (Chopra and Meindl, 2006). These trends mainly lead to a reduction of total landed cost due to lower production (procurement) cost in the case of offshoring and outsourcing or lower inventory cost due to risk pooling in the case of physical centralization. But as a negative sideeffect supply chains are longer and/or more complex (Tang, 2006). Due to the increased length of supply chains more transportation activities are necessary leading to an increase of the respective costs. In this paper we will especially pay attention to the effect of transportation activity within a supply chain.

8.3 New Logistics Trends: Integrated Perspective The presented logistics trends have proven to be optimal for industrial companies under economic considerations. Recently studies have shown that the focus on the cost aspect of a certain strategy is no longer sufficient. Environmental criteria become more and more important for the decision-making of individual enterprises. Walker et al (2008) differ between internal (organizational factors, efficiency improvements) and external drivers (regulation, customers, competition and society) which may induce the consideration of environmental aspects in supply chain decision-making. Especially carbon dioxide (CO2) emissions heavily accelerate the greenhouse effect; 60% of this effect is caused by CO2. This is a reason why governmental institutions (UN, EU, etc.) often focus their regulations on CO2-reduction (Kyoto protocol, EU emission trading scheme, etc.). Furthermore, the risk which is related to these strategies is often not taken into account or underestimated. There are various types of risks that exist especially in the case of offshoring. Currency risk and political risk depend on the economic and political stability within a country. Intellectual property risk and competitive risk should also not be ignored (Van Mieghem, 2008). Ferreira and Prokopets (2009) conclude from the “2008 Archstone/SCRM Survey of Manufacturers” (in-depth survey of 39 senior executives from US and European-based manufacturers) that executives also start to recognize aspects of offshoring, such as “quality problems, longer supply chains, lack of visibility, piracy and intellectual capital theft”. Due to these additional aspects the cost savings of offshoring which represent between 25% and 40% on average start to diminish. In addition, an offshoring strategy negatively affects the flexibility and responsiveness of a supply chain as shipments have to be made in large lots (e.g. containersize) and the delivery time is very long (e.g. up to several months). Besides, the customization of products to individual customer needs is more difficult. Furthermore, the cost components are about to change; 40% of the manufacturing enterprises have


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experienced an increase of 25% or more in direct costs of offshoring (materials, components, logistics and transportation) over the last three years. Nearly 90% of them expect costs to rise by more than 10% in the next 12 months. This is due to increasing labor costs in important offshore countries, like China (2005-2008: wages + 44%), an increase in transportation charges for sea freight (2005-2008: freight charges + 135%) and a non-favorable development of foreign currencies (Ferreira and Prokopets, 2009). Furthermore, Simchi-Levi et al (2008) point out that even though the oil price has decreased recently it is likely that it will increase again above $100 a barrel in the year 2009. Offshoring, outsourcing and centralization result in supply chains which are costefficient, but as a negative side-effect they are longer and/or more complex (Tang, 2006). Due to the increased length of supply chains more transportation activities are necessary; even though some of the transport can be shifted to more environmental friendly modes, such as sea transport, in total, these trends have a negative impact on the environment. Similar conclusions can be drawn with respect to the risk dimension. The more extended a supply chain is, the more risk it has to bear and the more difficult it is to guarantee a certain delivery reliability. It can be concluded that in the future the existing trends have to be reconsidered; environmental criteria and the risk dimension will become more important. Further, the cost structure is expected to change. These shifts in priorities of companies as well as the shifts in the cost components force companies to search for new logistics strategies that are at the same time cost-efficient, environmental friendly and reliable. Supply chain risks as well as environmental aspects should be considered, besides economic criteria, in the performance evaluation of a supply chain. Based on this integrated perspective new logistics trends have come up recently and will gain more importance in the near future. Through network redesign, i.e. by moving production activities back or closer to the market through near-, onshoring or decentralization, the transportation distances can be reduced. The study of Ferreira and Prokopets (2009) shows that 30% of the companies surveyed have already reversed their offshoring decision; 59% are willing to change their strategy with respect to offshoring. This means that either offshored activities are relocated or that managers will show an increased awareness in future offshoring decisions. For instance, a company from the apparel industry which produces casual wear, sportswear and underwear in two manufacturing sites in the US considered redesigning its network in order to reduce its CO2-emissions. For inbound transportation rail and trucks were used whereas on the outbound side the company completely relied on road transportation. The moving of some production activity to a low-cost site in Mexico and the introducing of new distribution sites was evaluated considering cost and CO2-emissions. The optimization only with respect to cost led to a moving of production activity to Mexico and the installation of two additional distribution centers; total costs reduction (costs for warehouse and production sites, transportation and inventory) amounted to 16%, nearly US$ 8 million in absolute figures, and CO2-emissions could be lowered by 5%. Then, a reduction of CO2-emissions by 25% was introduced as constraint. Now, nearly no production activity was dislocated to Mexico, thereby producing closer to the

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market and reducing transportation distances. This new network design resulted in a small increase of total costs compared to the optimal solution, but the total costs are still more than 10% smaller than in the initial situation and the CO2-emissions could be reduced by a quarter (Simchi-Levi, 2008). Concerning supply chain risks, it has to be pointed out that offshoring, outsourcing and centralization typically move production away from the market which reduces the responsiveness and flexibility of a supply chain. This has to be considered together with the possible cost reductions of a certain strategy (Allon and Van Mieghem, 2009). Further, Tang (2006) points out that supply chains have to become robust which means that a supply chain is able to fulfill customer requirements even though a disruption of the supply chain has occurred. This disruption can be of different kind, either a short one due to congestion or accidents or a long one which can be the result of a natural disaster or a terrorist attack destroying one node or arc in the supply chain. By using a flexible supply base a company can benefit from low costs in an offshore facility and simultaneously be able to respond quickly to demand fluctuations by serving the market also from an onshore site and react to delivery delays and disruptions. In this way, the amount of long-distant transport can be reduced, therefore mitigating transportation risks. For instance, Hewlett Packard uses an offshore facility to produce the base volume and employs also an onshore facility to quickly react to disruptions and demand fluctuations (Tang, 2006). Furthermore, flexible transportation helps to improve the performance of a supply chain by a change of transport mode, multi-modal transportation or the use of multiple routes. The use of a single mode is mainly due to cost consideration and the aim to reduce complexity in supply chains but this increases the vulnerability of the supply chains. By using multi-modal transportation the supply chain is able to obtain more flexibility and therefore can handle disruptions easier. Especially in the case of congestion an alternative route could increase the time- as well as costeffectiveness. For instance, LKW Walter decided to change the mode on the link north-eastern Spain to southern Italy. Road transportation was replaced by a multimodal solution (sea/truck). Thereby, 1,211 km per shipment (1,523 km on the road vs. 312 km short sea/trucking), in total over 1.2 million km per year, could be saved (ECR, 2008). Nike operates a distribution center in Belgium that serves the European market. 96% of the freight to the location is transported by inland waterways. Thereby, 10,000 truck loads could be saved and also on the distribution side Nike very much relies on waterways; only the direct delivery to the customers is carried out by truck (Seebauer, 2008). Improvements in transportation efficiency can be achieved through better vehicle utilization, the reduction of empty trips as well as less frequent shipments with larger lot sizes. This leads to a reduction of the number of transports. Thus costs, CO2-emmissions and fossil fuel consumption can be reduced significantly. S.C. Johnson & Son Inc., a household and personal-care products maker, for instance, was able to cut fuel use by 630,000 liters by improving truckload utilization (Simchi-Levi et al, 2008). By maximizing full truck load and supplying the market from the closest location, PepsiCo, on average, saved 1.5 million km and 1,200 t


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CO2-emissions (ECR, 2008). The British drugstore chain Boots, for instance, could avoid empty runs by using route planning. Thereby, 2.2 million kilometers on the road could be eliminated which resulted in a reduction of 1,750 t CO2-emissions. In combination with the use of larger containers, increased utilization of the containers and reduced amount of air transportation Boots achieved a reduction of 3,000 t CO2 (-29%) between 2004 and 2007. These improvements were only possible due to the tight collaboration between Boots and its logistics service provider Maersk Logistics (Seebauer, 2008). According to Simchi-Levi et al (2008) logistics service providers will be employed more often in order to increase efficiency. They are able to consolidate the shipments from a large number of customers and therewith can reduce the number of empty trips. Again Boots was able to save approximately 120,000 km as well as 92 t of CO2-emissions per year by sharing transportation with another company in the UK. Further examples in this context can be found in the ECR Sustainable Transport Project (ECR, 2008). Table 8.1 gives an overview of the presented new logistics trends. In the following sections we use the flexible supply base - one of the presented new logistics trends - to develop a transport-focused framework and a stylized model for dual sourcing.

8.4 Transport-Focused Framework for Dual Sourcing In the previous section it was exemplarily shown that a flexible supply base can help to improve the performance of a supply chain from an integrated perspective including economic, risk and environmental criteria. In the following we will focus on a certain type of this strategy, i.e. dual sourcing depending on a cheap but inflexible and slow offshore supply source and on an expensive but flexible and fast onshore supply source. The onshore supply source can help to improve the performance of a supply chain with respect to risks in two cases, to bridge delivery delays and/or disruptions or to fulfill demand exceeding the offshore order quantity. Table 8.2 gives an overview of the external conditions that have an impact on a company’s policy and the decisions to be taken. Environmental regulations, like the emission trading scheme of the EU, impose restrictions on companies and therefore influence the policies they choose. The emission trading scheme of the EU (EU ETS) was implemented in order to reach the goals stated in the Kyoto protocol. It is a cap-and-trade system of allowances for emitting CO2 and other greenhouse gases whereby each allowance certifies the right to emit one ton of CO2. Only certain industries are included in this regulation up-tonow. These industries are heavy energy consuming industries, like refineries, power generation with fossil resources, metal production and processing, pulp and paper, etc. Today, 11,000 sites that produce around 50% of the EU’s total CO2-emissions are covered by the EU ETS. A certain number of emission allowances are allocated to the companies free of charge. Those companies that produce fewer emissions than the number of allowances owned can sell them, whereas those producing more have

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Table 8.1 Overview of new logistics trends: Integrated perspective Logistics trends

Characteristics

Relevance on in- Case study tegrated perspective

Network redesign

Nearshoring, Reduced Onshoring, transportation Decentralization distances and number of transports

Using regional distribution centers, a company from the metal manufacturing industry was able to reduce the average distance to customer by 46%.In the apparel industry, the decision to produce at an onshore facility reduced CO2emissions by 25%.

Flexible supply base

Using multiple supply sources (offshore and onshore)

Reduced number of long-distant transports and mitigation of transportation risks

Hewlett Packard uses an offshore facility to produce the base volume and employs also an onshore facility to quickly react to disruptions and demand fluctuations.

Flexible transportation

Change of transport mode, Multi-modal transportation, Multiple routes

Reduced CO2-emissions and dependence on fossil fuels, Reaction to occurrence of risk events

LKW Walter saved 1,211 km per shipment by changing the mode (1,523 km on the road vs. 312 km short sea/trucking), in total over 1.2 million km per year.

Transportation efficiency

Vehicle routing and loading, Consolidated shipments

Reduced number of empty trips, Improved, vehicle utilization

By maximizing full truck load, PepsiCo, on average, saved 1.5 million km and 1,200 t CO2-emissions. A manufacturer of household and personal-care products cut fuel use by 630,000 litres by combining multiple customer orders.

Table 8.2 Transport-focused framework for dual sourcing External conditions

Environmental regulations (emission trading scheme) Transportation network including transportation risks

Policies

Dual sourcing (off- and onshore supply source)

Decisions

Offshore order quantity Emission allowances

to buy additional allowances, get credits by engaging in emission-saving projects or have to pay a penalty. The aim is to reduce the number of allowances constantly, so as to decrease the total CO2-emissions within the EU (-21% until 2020). In 2006, half of the greenhouse gases in the EU are caused by industry; the second largest “polluter” is transportation accounting for nearly 20%. The EU is already planning to increase the number of companies and sectors which have to comply with the trad-


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ing scheme, e.g. include civil aviation by 2013 (EC, 2008). So, it has to be expected that the whole transport sector will be confronted with more severe regulations or the inclusion into the EU ETS in the near future. External conditions are also determined by the transportation network including respective risks. According to Rodrigues et al (2008) transportation risks are related to the carrier who executes the transport and to external factors. The carrier is a source of risk with respect to his fleet capacity, network planning, scheduling and routing and information system as well as his financial conditions and reliability. As external risk factors, transport macroeconomics (oil price, availability of drivers, etc.), infrastructure conditions (congestion, construction, etc.) and future government policies have to be mentioned. Further, severe shocks, like terrorist attacks, natural disasters or industrial action, might have a strong impact on the transportation network. Whereas the probability of such event is very low, the impacts can be detrimental. Based on this, they state that with the increasing degree of outsourcing and the higher geographical spread of supply chains the transportation risks increase (Rodrigues et al, 2008). The paper by Allon and Van Mieghem (2009) about global dual sourcing shows that it is almost impossible to derive the optimal sourcing policy for a responsive near-shore source and a low-cost offshore source even if the criterion is just cost minimization. By including an environmental criterion, thus, it seems reasonable to develop a simple model for dual sourcing with onshore reactive capacity to be able to analyze the consequences for the offshore order quantity.

8.5 Single-Period Dual Sourcing Model Including Emission Costs In the seminal newsvendor model a possibility to reduce the mismatch cost of understocking or overstocking is to allow for a second order opportunity. In the simplest version it is assumed that at the beginning of the selling season the demand of a product is known exactly or that the second production facility can immediately produce any requested quantity (see e.g.,Warburton and Stratton, 2005 or Cachon and Terwiesch, 2009, chapter 12). In the considered single-period dual sourcing model a product can either be sourced from an offshore production facility and from an onshore production plant whereby the capacity of the onshore supply source is unlimited and can deliver immediately. The two suppliers can be internal or external to the company. Because of the long procurement lead time the offshore order quantity of the product is based on the random demand X characterized by the distribution function F. The company, e.g. a retailer, sells the product at the unit selling price p. The purchase price per unit from the offshore supplier is denoted by co f f , that from the onshore supplier is con . Leftover inventory at the end of the regular selling season can be sold at a unit salvage value z. It is assumed that p > con > co f f > z holds. Then the profit P depends on the offshore order quantity q and on the realized demand x:

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P(q, x) =

px − co f f q + z(q − x)+ x ≤ q px − co f f q − con(x − q)+ x > q

The optimal offshore order quantity q∗ is derived by maximizing the expected profit E(P(q, X)). Using the framework of the classical newsvendor model the optimality condition is given by (see, e.g. Cachon and Terwiesch, 2009, section 12.4): F(q∗ ) =

con − co f f con − z

The unit purchase price from the offshore supplier is composed of the product price per unit c and the emission cost factor ϕ ; the unit purchase price from the onshore supplier is obtained by adding a domestic premium (d · c) to the offshore product price per unit. This premium mainly is caused by higher labor costs that have to be paid in the onshore production facility (Warburton and Stratton, 2005). The two cost parameters are defined as : co f f = (1 + ϕ )c, con = (1 + d)c. The offshore supply source is only used if it is overall cheaper than the onshore supply source, which is the case as long as ϕ < d. As soon as d ≥ ϕ the product quantity is exclusively procured from the onshore source on order. The factor ϕ represents the emission costs per product unit, whereby it is assumed that costs for emission allowances only arise for long-distant transportation from the offshore location. The emission costs per unit sourced from the offshore supplier depend on the selected transportation route and transportation mode. For the different modes average emission factors per kilometer exist. Multiplying these emission factors with the distance the vehicle has to travel, the CO2-emissions for one trip can be calculated. The emission costs, then, are derived from the buying price of an emission allowance, traded under the EU ETS. It is reasonable to assume that the emission cost factor ϕ is independent of the order quantity q if the transport is carried out by a logistics service provider. The company, e.g. retailer, then has to reserve a fixed transport capacity which determines the factor ϕ . If part of that reserved capacity is not used by the company, the logistics service provider can sell it to other customers and therefore usually achieve high vehicle utilization. A numerical example with the following cost and price parameters is presented in order to show the impact of emission costs on the quantity decisions: selling price p = 20, product price per unit c = 10, salvage value z = 5 and domestic premium d = 0.2. The emission costs factor ϕ is varied in order to show the impact of increasing environmental costs on the optimal decision. Demand is assumed to be normally distributed with a mean μ of 1,000 units whereby two different standard deviations (σ1 = 150, σ2 = 300) are used in order to show the impact of variability. Taking a normally distributed demand is justified if the coefficient of variation (σ /μ ) is small enough (Warburton and Stratton, 2005). The offshore order quantity depends on the relative cost advantage that can be achieved through offshore sourcing. The lower the offshore cost is the more the


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retailer will procure from the offshore source. The onshore supply source is only employed in order to fulfill the demand that exceeds the offshore order quantity, i.e. expected lost sales. Therefore, with the onshore supply source a service level of 100% can be guaranteed. But it should not be forgotten that this comes at a high domestic premium. Nevertheless, the dual sourcing strategy often outperforms a pure offshoring strategy with respect to expected profit (see, e.g. Cachon and Terwiesch, 2009). With increasing emission costs (ϕ · c) the company sources less from offshore as the cost advantage is reduced. The offshore quantity decreases nearly linearly with increasing ϕ until a certain point after which it decreases sharply. The total order quantity (off- and onshore quantity) also decreases depending on ϕ . This is due to the following fact: The fewer units are procured through the offshore supply source the lower is the expected leftover inventory (I). The whole expected lost sales quantity (qon) is then fulfilled from the onshore supply source and this decision is taken under complete certainty. Overall, the total order quantity converges to the mean demand because q∗ + qon = E(X) + I Higher demand uncertainty, i.e. a higher coefficient of variation of demand, implies that the onshore supply source is used more. The numerical results for the two different demand distributions with the above price and cost parameters are graphically shown in Fig.8.1 and Fig.8.2. The emission costs factor is varied in the range 0 ≤ d < ϕ .

Fig. 8.1 Off-, onshore and total order quantity depending on the emission cost factor ϕ for normally distributed demand with μ = 1, 000, σ1 = 150 and d = 0.2

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Fig. 8.2 Off-, onshore and total order quantity depending on the emission cost factor ϕ for normally distributed demand with μ = 1, 000, σ1 = 3000 and d = 0.2

The presented model is based on limiting assumptions with respect to the existing environmental regulations concerning emission allowances. Under the existing EU ETS companies receive allowances free of charge. Therefore, in contrast to the model presented, emission costs do not arise for each unit ordered, but only if a certain threshold is exceeded. For a more general model with a positive emission limit and the opportunity to buy additional emission allowances or to sell unused ones we refer to Rosiˇc and Jammernegg (2009).

8.6 Summary Prevalent logistics trends, i.e. outsourcing, offshoring, and centralization are presented from a cost perspective. These strategies are chosen with the objective to reduce total landed costs (e.g. reduction of labor costs through offshoring or inventory costs through centralization). But as direct consequence transportation distances increase; supply chains become longer and/or more complex. This has negative impacts on the risk a supply chain has to face (e.g. congestion on transportation links) and on the environment (e.g. CO2-emissions). An integrated perspective is presented and new logistics trends which perform better with respect to transportation risks and the environment are illustrated by several case studies. Further, we use one of the presented trends - flexible supply base - to develop a transport-focused framework for dual sourcing. Dual sourcing means that a company relies on a cheap but slow offshore supply source and on an expensive but fast and unlimited onshore supply source. The external conditions which influence the policies of an individual


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company are environmental regulations focusing on the emission trading scheme for CO2-allowances of the EU and the transportation network including the respective risks. Then, a single-period dual sourcing model is presented. The objective is to maximize expected profit and it has to be decided how much to order from the offshore source; the onshore source is used in order to fulfill the demand exceeding the offshore order quantity. The costs for emission allowances are included in the offshore purchase price as for the quantity procured from the offshore supply source more transportation activity is necessary. It is shown that with increasing emission costs the offshore order quantity decreases, whereas the onshore order quantity increases and the total order quantity converges to the expected demand. The presented model is based on limiting assumptions with respect to the existing environmental regulations for emission allowances. For a more general model with a positive emission limit and the opportunity to buy additional emission allowances or to sell unused ones we refer to Rosiˇc and Jammernegg (2009).

References Allon G, Van Mieghem J (2009) Global Dual Sourcing: Tailored Base Surge Allocation to Near and Offshore Production. Tech. rep., Working Paper, Kellogg School of Management, Northwestern University Breinbauer A, Haslehner F, Wala T (2008) Internationale Produktionsver¨ lagerung Osterreichischer Industrieunternehmer Ergebnisse einer empirischen Untersuchung. Tech. rep., FH des bfi Wien, URL http://www.fhvie.ac.at/files/2008 Studie Produktionsverlagerungen.pdf Cachon G, Terwiesch C (2009) Matching supply with demand: An introduction to operations management, 2nd edn. McGraw-Hill, Boston Chopra S, Meindl P (2006) Supply chain management, 3rd edn. Pearson Prentice Hall, New Jersey Dachs B, Ebersberger B, Kinkel S, Waser B (2006) Offshoring of production A European perspective. URL http://www.systemsresearch.ac.at/%20getdownload.php?id=154 EC (2008) EU action against climate change The EU Emissions Trading System. European Commission. URL http://ec.europa.eu/environment/climat/pdf/brochures/ets en.pdf ECR (2008) ECR Sustainable Transport Project Case Studies. URL http://www.ecrnet.org/05-projects/transport/Combined%20Case%20studies v1%208 220508 pro.pdf Ferreira J, Prokopets L (2009) Does offshoring still make sense? Supply Chain Management Review 13(1):20–27 Rodrigues V, Stantchev D, Potter A, Naim M, Whiteing A (2008) Establishing a transport operation focused uncertainty model for the supply chain. International Journal of Physical Distribution & Logistics Management 38(5):388–411

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Rosiˇc H, Jammernegg W (2009) The environmental sustainability of quick response concepts. Working paper, Department of Information Systems and Operations, Vienna University of Economics and Business ¨ Seebauer P (2008) Supply Chain unter der Oko-Lupe. Logistik heute 2008 (10):54– 55 Simchi-Levi D (2008) Green and supply chain strategies in a volatile world. Fachkoferenz: Grüne Supply Chains, Frankfurt/Main, Germany Simchi-Levi D, Nelson D, Mulani N, Wright J (2008) Crude calculations. URL http://online.wsj.com/article/SB122160061166044841.html Tang C (2006) Robust strategies for mitigating supply chain disruptions. International Journal of Logistics: Research and Applications 9(1):33–45 Van Mieghem J (2008) Operations Strategy: Principles and Practice. Dynamic Ideas, Charlestown Walker H, Di Sisto L, McBain D (2008) Drivers and barriers to environmental supply chain management practices: Lessons from the public and private sectors. Journal of Purchasing and Supply Management 14(1):69–85 Warburton R, Stratton R (2005) The optimal quantity of quick response manufacturing for an onshore and offshore sourcing model. International Journal of Logistics, Research and Applications 8(2):125–141

Chapter 9

An Integrative Approach To Inventory Control Philip Hedenstierna, Per Hilletofth and Olli-Pekka Hilmola

Abstract Inventory control systems consist of three types of methods: forecasting, safety stock sizing and order timing and sizing. These are all part of the interpretation of a planning environment to generate replenishment orders, and may consequently affect the performance of a system. It is therefore essential to integrate these aspects into a complete inventory control process, to be able to evaluate different methods for certain environments as well as for predicting the overall performance of a system. In this research a framework of an integrated inventory control process has been developed, covering all relations from planning environment to performance measures. Based on this framework a simulation model has been constructed; the objective is to show how integrated inventory control systems perform in comparison to theoretical predictions as well as to show the benefits of using an integrated inventory control process when evaluating the appropriateness of inventory control solutions. Results indicate that only simple applications (for instance without forecasts or seasonality) correspond to theoretical cost and service level calculations, while more complex models (forecasts and changing demand patterns) show the need for tight synchronization between forecasts and reordering methods. As the framework describes all relations that affect performance, it simplifies the construction of simulation models and makes them accurate. Another benefit of the framework is that it may be used to transfer simulation models to real-world applications, or vice versa, without loss of functionality.

Philip Hedenstierna Logistics Research Group, University of Skövde, 541 28 Skövde, Sweden Per Hilletofth, Corresponding author Logistic Research Group, University of Skövde, 541 28 Skövde, Sweden, Tel.: +46 (0)500 44 85 88; Fax: +46 (0)500 44 87 99, e-mail: [email protected] Olli-Pekka Hilmola Lappeenranta Univ. of Tech., Kouvola Unit, Prikaatintie 9, 45100 Kouvola, Finland

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Philip Hedenstierna, Per Hilletofth and Olli-Pekka Hilmola

9.1 Introduction The purpose of inventory control is to ensure service to processes or customers in a cost-efficient manner, which means that the cost of materials acquisition is balanced with the cost of holding inventory (Axsäter, 1991). This is done by interpreting data describing the planning environment, i.e. the parameters that may affect the decision, to generate replenishment order times and quantities (Mattsson, 2004). The performance of an inventory control system may then be measured by the service and the total cost caused, when applied in a certain environment. Inventory control methods may be classified by whether they determine ordering timing, quantity, or both (Mattsson and Jonsson, 2003). For systems that determine only one aspect, such as the reorder point system or the periodic ordering system, the undetermined aspect must be calculated beforehand, typically using the economic order quantity or the corresponding economic inventory cycle time (Waters, 2003). The parameters that inventory control systems are typically including such things as demand forecasts, projected lead times, holding rates and ordering costs. Of these, the forecast is of special concern, as it is not a part of the planning environment, but a product thereof. This makes forecasting, given our definition of inventory control, an integral part of the inventory control system. To maintain service when there is forecast and lead time variability, safety stock is used, which is based on variability and on the uncertain times relating to the used inventory control model (Axsäter, 2006). As the safety stock incurs a holding cost, it may be argued that it should be part of the timing/sizing decision; however, it is usually excluded as optimization in most cases only gives insignificant cost savings (Axsäter, 2006). However, in larger distribution systems reduction of safety stocks is one primary driver of centralization of warehouses to one location (e.g. demand pooling, square root law, see Zinn et al 1989 and Das and Tyagi 1999) these could concern feeding warehouses of factories (Rantala and Hilmola, 2005, e.g.) as well as retail related distribution operations (Leknes and Carr, 2004, e.g.). We have now discussed three interdependent areas that are usually treated individually. They are all part of the interpretation of the planning environment to generate replenishment orders, and may consequently affect the performance of the system. The current approach to inventory control does generally not consider it as a single system, but as separate methods (e.g. Axsäter 2006, Waters 2003, Mattsson and Jonsson 2003 and Vollmann 2005). An exception is Higgins (1976), who describes inventory control as a process (see Fig.9.1), but does not detail how information flows through the model, nor does he isolate the functions of forecasting, safety stock sizing and inventory control. Looking at Higgins model, it is easy to realize that corruption of data occurring in an operation or between operations will cause the incorrect data to affect subsequent operations (Ashby, 1957). When theoretical models are applied to scenarios that follow the assumptions of the models, this is not an issue; but when a model is applied to a scenario it is not designed for, data corruption ensues. Applied to inventory control, this may mean that a simple forecast or a simple inventory control method is applied in an environment that does not reflect the method’s assumptions

9 An Integrative Approach To Inventory Control

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(The popularity of using simple methods, like the reorder point method is shown in Jonsson and Mattsson 2006 and Ghobbar and Friend 2004). When a method’s assumptions are unmet, its performance may be difficult to predict. The scenario of using theoretically improper methods is not unlikely, as businesses may want to utilize inventory control methods that are simple to manage, such as the reorder point system, even when the planning environment would require a dynamic lotsizing method such as the Wagner-Whitin, Part-period or the Silver-Meal algorithm (Axsäter, 2006). In the same fashion, simple forecasting methods may be applied to complex demand patterns to simplify the implementation and management of the forecasts.

Fig. 9.1 Higgins inventory control process model (Higgins, 1976)

To understand how a method will respond to an environment it was not designed for, it is necessary to understand the entire process, from planning environment to measurement of results. As it may be difficult to predict how a system based on a required type of input will react to unsuitable data, a model of the system may help to give insight into the system’s performance. In his law of requisite variety, Ashby (1957) states that a regulatory system must have at least as much variety as its input to fully control the outcome; applied to the inventory control process, this means that all aspects of a system must be modeled to get an accurate result. Inventory control systems consist of three types of methods: forecasting, safety stock sizing as well as order timing and sizing (Axsäter, 2006). Though there are many individual methods, only one method of each type may be used in an inventory control system for a single stock-keeping unit. In this research a framework of an integrated inventory control process has been developed, covering all relations from planning environment to performance measures. The design of the framework was based on a literature review of inventory control theory and on the authors’ experience of the area. Based on this framework a simulation model has been constructed considering demand aggregation, forecasting, and safety stock calculations, as well as reordering methods. The research objective of this study is to provide an increased understanding of the following research questions: (i) ‘How may the process of inventory control be described in a framework that allows for any combination of methods to be used?’, and (ii) ‘Is there any benefit of integrated inventory control when deciding appropriate inventory control solutions?’.

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The remainder of this paper is structured as follows: First, Section 9.2 integrates existing theory to describe a framework for designing inventory control models. Section 9.3 introduces empirical data from a company, whose planning environment was interpreted in Section 10.2.2 to develop a simulation model based on the framework. Section 9.5 describes the results of the simulations. Thereafter, Section 23.5 discusses the implications of the results, while Section 18.5 describes the conclusions that can be drawn from the study.

9.2 Framework for Integrated Inventory Control The design of the framework is based on observing how inventory control methods operate, what input they require and what output they provide. An underlying assumption for inventory control systems is that there for any given time t, is an inventory level LL, which is reduced by demand D and increased by replenishment R. Another assumption is that time is divided into buckets as described by Pidd (1988), for continuous systems buckets are infinitesimal, and that for each bucket the lowest inventory level, which is sufficient to evaluate the effects of inventory control, is governed by Formula 1. The relationship between these factors has been deduced from the rules that material requirements planning is built on (Vollmann, 2005). LLt = LLt−1 + Rt−1 − Dt

(9.1)

where LLt = lowest inventory level at time t,Rt−1 == replenishment quantity occurring before t and Dt = demand during t. Formula 1 dictates how transactions of any system placed in the framework will operate. It considers replenishment to occur between time buckets, meaning that it is sufficient to monitor the lowest inventory level to manage inventory transactions. Information such as service levels, inventory position and the highest stock level may be calculated from the lowest inventory level. The formula governs the inventory transactions of any inventory control system, and must be represented in any inventory control application. All other parts of an application may vary, either depending on the planning environment in which an inventory control system is used, or on the design of the system. Fig. 9.2 shows the framework, which starts with the planning environment and ends with a measurement of the system’s performance. The planning environment comprises the characteristics of all aspects that may affect the timing/sizing decisions (Mattsson, 2004). For each time unit, the environment, which determines the distribution of demand, generates momentary demand that is passed on to a forecasting method, to an inventory control method and to actual transactions. The type of demand, which is dictated by the planning environment, tells whether a backlog can be implemented or not, and what function that may represent it (Waters, 2003). Forecasting is affected by past demand information and the planning environment (Axsäter, 1991). The former is used to do time series


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analysis, which is common practice in inventory control, while the latter may concern other input, such as information that may improve forecasting or data needed for causal forecasting. The environment may also tell of changes in the demand pattern, which may necessitate adjusting forecasting parameters or changing the forecasting method. It is necessary to consider the aggregation level of data, as longer term forecasts will have a low coefficient of variation, at the cost of losing forecast responsiveness (Vollmann, 2005). Forecast data is necessary for inventory control methods (forecasted mean values), and for safety stock sizing (forecast variability) (Waters, 2003). Safety stock sizing is a method buffering against deviations from the expected mean value of the forecast (Waters, 2003). The assumption of safety stock sizing is that all forecasts are correct estimations of the future mean value of demand; any deviations from the forecast are attributed as demand variability. This effectively means that an ill-performing forecast simply detects higher demand variability than a good forecast. The sizing is also affected by the planning environment, as the uncertain time determines the need for safety stock, as lead times also may have variability, and as the environment will determine to what extent customers accept shortages, or low service (Axsäter, 1991). Inventory control methods rely on forecasts, on safety stock sizing and on the planning environment. The safety stock is used as a cushion to maintain service, while forecasts and data from the planning environment, which are ordering costs, holding costs and lead times, are used to determine when and/or how much to order (Vollmann, 2005). The actual balancing of supply, which comes from the replenishment of the inventory, and demand, which is sales or lost sales, takes place as inventory transactions. Measuring these transactions gives an understanding of how well an inventory control system performs for the given planning environment (Waters, 2003).

9.3 Empirical Data Data was collected from a local timber yard, currently not using an inventory control policy. Existing functionality for the reorder point method and for the periodic order quantity method allowed for these methods to be deployed at low cost. The issue was whether the methods could cope with the fluctuations in demand, as trend and seasonal components were assumed to exist. Based on an analysis of sales data, the demand for timber was found to be seasonal, but with no trend component. This information was used to generate a demand function, based on the normal distribution. The purpose of the demand function was to allow the simulation model to run several times (200 independent simulations of three consecutive years were run, with random seeds for each simulated day). Real demand, as well as a sample of simulated demand, is shown in Fig. 9.3. Demand characteristics are shown in Table 9.1 and other parameters pertaining to the planning environment are shown in Table 9.2. As transport costs were considered to be semi-fixed rather than variable, the reordering cost is valid for the reorder

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Fig. 9.2 Framework describing relations within inventory control systems

quantity used. Increasing the order quantity was not a cost-effective option. Stock out costs were not considered, as the consequences of stock outs are hard to measure; not only are sales lost, there is also the possibility of competitors winning the sale, and of losing customers, as they cannot find what they need. Lead times were considered as fixed, as no information on delivery timeliness was available. The expected fill rate (fraction of demand serviceable from stock) for the reorder point method was 99%, while the it for the periodic order quantity method would be 98% and for the lot-for-lot method would be 96% (calculated


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Fig. 9.3 Simulated and actual monthly demand Table 9.1 Demand characteristics Demand Year Month Day

μ σ

56316 4693 156 710 205 37

Table 9.2 Environmental parameters Parameter Lead time (days)

Value 7

Reordering cost (SEK) 3200 Holding rate (%) 20% Unit cost (SEK) 4.49 Order quantity (ROP) Order interval (POQ) Order interval (L4L)

6500 45 7

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using the loss function, based on the standard deviation, as described by Axsäter (2006).

9.4 Simulation Model To test how the framework could be applied to a real-world scenario, a simulation model was constructed to evaluate inventory control solutions considered by a local timber yard. To support the inventory control systems, some simply managed forecasting systems were chosen. The complete selection of methods, put into the context of the framework is shown in Fig. 9.4.

Fig. 9.4 Methods placed in the framework

All methods were verified against theory by testing, if the method implementations gave the values that theory dictates. For the reorder point method, the reorder point was raised by days of forecasted demand, to prevent undershoot, as described in (Mattsson, 2007). Several forecast methods were considered, and the actual choice of forecast for this case was based on the mean absolute deviation.


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Bias was calculated to see whether a forecasting method followed the mean of demand. The seasonally adjusted moving average (Waters, 2003) was chosen as the preferred method, as it proved to be nearly as accurate as Holt-Winters (Axsäter, 1991), while not requiring as careful calibration. Table 9.3 Summary of forecast errors Type

EXP MA HOLT H-W S-MA

MAD 1281 1189 1267 179 263 Bias(%) 0.9% 0.3% 0.5% 0.1% -0.5%

Forecasts were monthly, and predicted the demand for the following month. The forecast value was multiplied by 1.5 to reflect an economic inventory cycle time of 45 days. This simplification was done to see how the system would react to systematic design errors.

9.5 Simulation Results To investigate how seasonality affects the performance of simple planning methods, variations of the presented demand pattern were simulated. In the first, demand was constant (Case 1); in the second, variance was added (Case 2), while in the third, seasonality (±20%) was introduced (Case 3). For the different cases a moving average forecast was used, adjusted for seasonality. Ignoring safety stock altogether, the measures used for the simulations were fill rate and inventory cycle service level. It should be noted that lot-for-lot has a different inventory cycle from the other reordering mechanisms, meaning that its service levels cannot be directly compared to them. Fig. 9.5 shows the results of the simulation runs. What can be seen is that inventory cycle service is higher for the periodic order quantity method than for the reorder point method. However, the fill rate shows that the reorder point method is better at meeting demand. Together, the measures tell that the periodic order quantity method has fewer, but greater stock-outs than the reorder point method. Seasonality affected the fill rate of the periodic order method the worst, while the reorder point method was hardly affected. The final situation added the seasonal pattern of the original data, and considered another inventory control solution, namely lot-for-lot. The result is shown in Figure 9.6, which is the fill rate and the holding cost incurred, compared to the theoretical fill rate, should no seasonality or forecast error be present. The periodic order quantity system shows a considerably worse fill rate than the reorder point system. The lot-for-lot system has a much lower holding cost than the other two methods due to more frequent orders; however, safety stock accounts for a larger fraction of the total holding, than for the other methods, leading to higher safety stock costs per stored unit. Observing the graphs, the lot-for-lot method is the only method where the mea-

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Fig. 9.5 Cycle service levels and fill rates

sured cost/service relationship does not intersect with the theoretical function. For the methods with longer order cycles, the measured cost/service relationship shows a much flatter curve than expected, indicating that these functions will require more safety stock than expected to improve fill rates.

9.6 Discussion Completed simulations indicate that the fill rate of the periodic order quantity method suffers when the seasonal demand pattern is introduced, while the reorder point method can maintain the same fill rate as if no seasonality were present. This is a result of the nature of the two methods, where variability affecting the reorder point method will affect the time of ordering, while the periodic order quantity method, with fixed ordering times, cannot regulate order timing to prevent stock outs. Instead, it must let the inventory level take the full effect of any variability. Conversely, the effect of variability on the reorder point method is that the resulting order interval may not be economic. When comparing the methods used in the simulation using the framework, we find that the reorder point method is superior both concerning holding costs, and fill rate. What system is preferable depends on whether suppliers can manage to deliver varying quantities (up to three times the average, both for periodic ordering, and for lot-for-lot) or at varying intervals.


Fig. 9.6 Total inventory costs and fill rates

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The difference between measured and theoretical fill rate demonstrated by the periodic order quantity shows how inventory control methods not designed for a certain planning environment can be affected. The use of a monthly forecast not representing the next inventory cycle may also have contributed to the low fill rate. The simulation based on the framework helped give insight into how the inventory control process would react to the planning environment. It showed that a large safety stock would be required if the periodic order quantity were to be used, as the periodic order quantity method undershot performance predictions much more than the reorder point method. If applied over multiple products, the framework can tell if consolidation using the sensitive periodic order quantity system is less costly than the reorder point system. Given that the periodic order quantity system has a 100% uncertain time (Axsäter, 1991), it may be used as a benchmark in simulations, as variability and problems caused by poor design of the process always are reflected in the fill rate. In the future we plan to enlarge our simulation experiments by incorporating different kind of demand types (continuous and discontinuous) as well as new methods used in forecasting and ordering. Recent research has shown that autoregressive forecasting methods outperform others in situations where demand is fluctuating widely and follows a “life-cycle” pattern (Datta et al, 2009). Similarly, purchasing order method research argues that not a single ordering method should be used (so basically it is not a question, which method is the best one, but which one best suits the environment), but usually a combination of different purchasing methods should be incorporated in ERP systems during the entire life-cycle of a product (Hilmola et al, 2009). However, if volumes are low, then even economic order quantities/reorder point systems, and periodic order policies should be abandoned; a lot for lot policy might produce best results in these situations (Hilmola et al, 2009). Thus, much depends from the operations strategy (order or stock based system), and from the amount of time, which customers are willing to wait for a delivery to reach their facilities (Hilletofth, 2008).

9.7 Conclusions Treating inventory control and forecasting as separate activities, while not acknowledging how forecasting and its application affect inventory control may lead to incorrect assessments of a system’s performance in a certain planning environment. Approaching inventory control as a process, starting with a planning environment and ending with a measurement of the system’s performance shows that all activities are related, and that the end result may be affected by the activities or by the way they are connected. This paper uses a simulation model to show how the use of forecasts and complexity in demand patterns affects the performance of the reorder point system and the periodic order quantity system. Simulations show that performance generally is worse than expected, and that periodic ordering consistently shows a greater susceptibility both to variability and to design errors, due to its inability to


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buffer against these by changing the reordering interval. This weakness also appears in lot-for-lot systems, as they are based on periodic ordering.

References Ashby WR (1957) An Introduction to Cybernetics. London: Chapman & Hall, London, UK Axsäter S (1991) Lagerstyrning. Studentlitteratur, Lund, Sweden Axsäter S (2006) Inventory Control. Springer Verlag, New York, USA Das C, Tyagi R (1999) Effect of correlated demands on safety stock centralization: Patterns of correlation versus degree of centralization. Journal of Business Logistics 20:205–214 Datta S, Granger CWJ, Graham DP, Sagar N, Doody P, Slone R, Hilmola O (2009) Forecasting and risk analysis in supply chain management GARCH Proof of Concept. ESDCEE, School of Engineering, URL http://dspace.mit.edu/bitstream/handle/1721.1/43943/GARCH%20Proof%20of%20Conept%20 %20Datta Granger Graham Sagar Doody Slone Hilmola %202008 December.pdf?sequence=1 Ghobbar A, Friend C (2004) The material requirements planning system for aircraft maintenance and inventory control: A note. Journal of Air Transport Management 10(3):217–221 Higgins J (1976) Information systems for planning and control: Concepts and cases. Edward Arnold, London, UK Hilletofth P (2008) Differentiated Supply Chain Strategy Response to a Fragmented and Complex Market. PhD thesis, Chalmers University of Technology, Department of Technology Management and Economics, Division of Logistics and Transportation, Gteborg, Sweden Hilmola OP, Ma H, Datta S (2009) A portfolio approach for purchasing systems: Impact of switching point. Massachusetts Institute of Technology, no. ESD-WP2008-07 in Working Paper Series, URL http://esd.mit.edu/WPS/2008/esd-wp2008-07.pdf Jonsson P, Mattsson S (2006) A longitudinal study of material planning applications in manufacturing companies. International Journal of Operations & Production Management 26(9):971–995 Leknes H, Carr C (2004) Globalisation, international configurations and strategic implications: The case of retailing. Long Range Planning 37(1):29–49 Mattsson S (2004) Logistikens termer och begrepp. PLAN, Stockholm, Sweden Mattsson S (2007) Inventory control in environments with short lead times. International Journal of Physical Distribution & Logistics Management 37(2):115–130 Mattsson S, Jonsson P (2003) Produktionslogistik. Studentlitteratur Pidd M (1988) Computer simulation in management science. John Wiley & Sons, Hoboken, USA

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Rantala L, Hilmola O (2005) From manual to automated purchasing Case: Middlesized telecom electronics manufacturing unit. Industrial Management & Data Systems 105(8):1053 – 1069 Vollmann T (2005) Manufacturing planning and control systems for supply chain management. McGraw-Hill Waters D (2003) Inventory Control and Management. Wiley, Hoboken, USA Zinn W, Levy M, Bowersox D (1989) Measuring the effect of inventory centralization/decentralization on aggregate safety stock: The ’square root law’ revisited. Journal of Business Logistics 10(1):1–13

Chapter 10

Rapid Modeling of Express Line Systems for Improving Waiting Processes Noémi Kalló and Tamás Koltai

Abstract In time-based competition, one of the main management objectives in services is to decrease customers’ waiting. Accordingly, search for designs of queuing systems which reduce waiting has become a major concern of managers. A frequently used solution is the application of express lines. The operation of express line systems can be optimized based on different objective functions. The minimization of average waiting time and the reduction of the variance of waiting times are the classical objectives for operation managers. According to perception management, however, the perceived waiting times and satisfaction generated by waiting should be considered as well. To analyze the effects of different management objectives on the operation of express line systems, a numerical and a simulation model were developed. The study of a superstore shows that the rapid numerical model and the time-consuming simulation model provide the same result when the parameter values ensuring optimal operation must be determined. Consequently, in these problems, simulation can be substituted efficiently by rapid modeling.

10.1 Introduction Companies, which are successful in cost- and quality-based competitions, look for other factors that can help them to gain further competitive advantage. Therefore, time-based competition spreads among leading companies. Time has turned into Noémi Kalló Department of Management and Corporate Economics, Budapest University of Technology and Economics-Hungary, 1111 Budapest, Müegyetem rkp. 9. T. e´ p. IV. em. e-mail: [email protected] Tamás Koltai Department of Management and Corporate Economics, Budapest University of Technology and Economics-Hungary, 1111 Budapest, Müegyetem rkp. 9. T. e´ p. IV. em. e-mail: [email protected]

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a strategic resource and, as a consequence, its importance has become equivalent to the significance of money, productivity, and innovation (Stalk, 1988). That is, competitiveness nowadays requires balancing quality, cost, and time. In time-based competition environment, one of the main service management objectives is reducing waiting times. The simplest way for decreasing customer waiting is using additional servers (Hillier and Lieberman, 1995). This kind of waiting time reduction is, however, quite expensive. Consequently, search for the best configuration of waiting lines and service facilities has become a major concern of service managers (Hill et al, 2002). A queuing system configuration frequently used to reduce waiting times of some customers is the application of express checkouts. When express checkouts are applied, two customer groups are created: the first group consists of customers buying few items while all other customers belong to the second group. Customers buying more items than a certain number have to use the regular checkouts. Costumers buying less items than or equal quantity to this certain number can join the express lines. The number of items that controls line-type selection is called limit value. Our analyses revealed that one of the parameters which influence the waiting process when express lines are applied is the limit value. With different limit values, different waiting characteristics can be achieved. A suitable limit value can minimize a particular waiting characteristic. However, instead of the specific measures, the waiting process as a whole should be optimized. An important management objective connected to express line systems is to determine a limit value which optimizes the performance of the queuing system. This article presents tools to determine this value by reviewing some operational issues related to express line systems. The article is structured as follows. First, the tools developed for analyzing express line systems are presented. An analytical model (based on the results of queuing theory) and a simulation model (working according to the real process of a queuing system) are used for the analyses. For checking their validity, the real data of a do-it-yourself superstore was used. Next, different management objectives related to the service-profit chain, stretching from waiting minimization to satisfaction maximization, are discussed. Later, the results based on the case of the superstore are presented to compare the effects of the different management objectives on the performance of the system. Finally, the main conclusions are summarized.

10.2 Tools for Analyzing Express Line Systems Express line systems, like most queuing problems, can be modeled both analytically and empirically. Analytical models are based on the results of queuing theory. Generally some existing analytical models are used to approximate the operation of the queuing system. These models are quite simple to use; however, in the case of complex queuing systems, they give only rough estimation of the real operation. For analyzing these problems, new analytical models must be developed or simulation models can be used (Hillier and Lieberman, 1995). Simulation modeling requires

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more time and resource; however, quite special characteristics of queuing processes can be modeled in this way. For our analyses, an analytical and a simulation model were created as well.

10.2.1 Analytical Approach Queuing systems with express lines have several special characteristics which make their analytical modeling difficult. The most important specialty is that express lines are generally used in supermarkets where many service facilities are located and each has its own separate waiting line. Analyzing this kind of queuing systems with the models of queuing theory presents difficulties because there is no existing analytical model which can properly describe such a system. In this case, two analytical models can be used as approximations: one consisting of many service facilities with a common waiting line and another containing many independent queuing systems each having one service facility with its own separate queue. If analytical formulae have to be used for the whole queuing system - containing k checkouts and k waiting lines -, the following two approaches can be used: One-common-line approach. For this, the queuing system can be modeled as if all checkouts had one common queue. For this, a G/G/k model can be applied or, according to the system characteristics, a special type of it (for example M/G/k or M/M/k). If there are E express and R regular checkouts, then a model with k=E and another with k=R are required. Modeling the checkout system as a queuing system with one common line for all checkouts is an optimistic approach. It underestimates the average waiting time by assuming optimally efficient queue selection of customers which minimizes their waiting times. That is, it supposes that customers always choose the queue in which their waiting time will be shortest, and if their waiting line moves too slowly, they jockey among the queues. In some cases, however, customers cannot behave in the most efficient way. If there are idle checkouts but jockeying to these lines is difficult, or jockeying does not provide considerable time savings, then customers do not change line. Consequently, the one-common-line approach provides a best-case estimate of the operation of the queuing system. Independent-queuing-system approach. In this case, k independent G/G/1 models are applied or, according to the system characteristics, other special models (for example M/G/1 or M/M/1). If there are E express and R regular checkouts, then E+R models are required. Modeling the checkouts of a supermarket as independent queuing systems gives a pessimistic approach of waiting since it overestimates the average waiting time. Waiting lines are, however, generally not independent from each other, which can help to reduce the average waiting time. First, most of the arriving customers try to join the shortest queue. Second, some customers jockey from slowly moving lines to fast moving ones. If, for example, some checkouts become idle, customers waiting in line try to jockey to the idle checkouts. That is, queues are not independent from

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each other. As a conclusion, the independent-queuing-system approach provides a worst-case estimate of the operation. It depends on the system characteristics, which of the presented approaches gives more accurate approximation of actual operation. If customers estimate the workloads of servers before selecting waiting line, the application of the one-commonline approach gives a better approximation (Rothkopf and Rech, 1987). For some reasons, however, customers do not always selects the queue with the minimal workload. For example, when workloads cannot be observed, the best decision cannot be made. In this case, the independent-queuing-system approach is more suitable. To create a numerical model for analyzing express line systems the approaches discussed above were used as best-case and worst-case estimations of waiting time. In Fig.10.1, a part of the numerical model can be seen - with the data of a do-ityourself superstore (Sec. 2.3).

Fig. 10.1 Numerical model

Introducing express lines into a queuing system requires the consideration of several operational issues. One of the main questions related to develop an express line system is to determine the limit value which optimizes the operation of the system. To make this decision, the effect of all possible limit values must be examined. As the limit value determines which customers use the express and which the regular checkouts, for this analysis, characteristics of customer groups generated with all possible limit values must be determined. These main characteristics are the arrival


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rates, the average service times and variances of service times. Before introducing express checkouts, this information is unavailable, that is, it must be determined by using the data of the existing system. For building the analytical - and the simulation - models only such information and data were used which can be determined without the actual introduction of the express lines. The data used can be obtained by observing and measuring the operation of the existing queuing system without express lines. Therefore, decisions about the implementation of express lines can be made in advance and the possible effects on customer waiting can be forecasted. For determining the service characteristics of different customers the relationship between the number of items bought and the service times must be analyzed. By using this relationship, the average service time and the variance of service times can be determined for customers buying a certain amount. With the help of the distribution function of the number of items bought, the average arrival and service rates, and the variances of services times can be calculated for all possible customer groups as well (for details see Koltai et al, 2008). The model works in the following way. Based on the main characteristics of the existing queuing systems (in italics), the special characteristics of the express line systems with different limit values are determined. With these parameters, using the formulae of M/G/1 and M/G/k queuing models, the average waiting times also can be calculated (typed boldface). Knowing all possible waiting times the smallest one must be selected (framed). The minimal average waiting time, eventually, determines the optimal limit value. Analyses with different parameter values showed that the waiting time as a function of the limit parameter has a distinct minimum. That is, an optimal limit value can be determined for every express line system (Fig.10.2).

Fig. 10.2 Waiting time as a function of the limit parameter

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10.2.2 Simulation Model Express line systems have several special characteristics, and only a few of them can be taken into consideration with analytical models. For example, the managerial regulation which controls the use of checkouts can be build into analytical models. If there are more than one checkout accessible for customers, their choice among them cannot be considered. The analytical model appropriate for describing express line systems assume either uniform customer distribution among accessible waiting lines (independent-system approach) or do not deal with line selection at all (onecommon-queue approach). A simulation model, considering several customer behavioral issues, was built for studying the operation of express line systems. The block diagram of the simulation model created with Arena, simulation software of Rockwell Automation, can be seen on Fig.10.3

Fig. 10.3 Simulation model

With the first, create block, customers are generated according to a stochastic distribution. The assign block, based on a formerly defined distribution function, determines the number of items bought by each customer. With this quantity, knowing their stochastic relationship, the service time of each customer is also calculated. The branch block creates two customer groups: one of them can use the express checkouts, the other are directed to the regular lines. Customers entitled to use express checkouts buy no more items than the limit value. Customers in each group have to make a decision about which line to choose. Rules forming the base of this decision can be given in the pickq blocks. Next, the customer joins the selected queue, waits until the server will be free and can be seized. At this point, the waiting process in queue ends. The waiting time is recorded by a tally block. The following branch block is needed for data collection and statistical analyses. The customer’s route continues along the solid lines while waiting time data of the same customer group are combined in tally blocks (along the dashed lines). As the service needs a specific amount of time, the customer is delayed. When service ends, the server


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is released and made free for the next customer. At this point the sojourn time ends and it is recorded by a tally as well. After combining the different waiting time data, the customer can leave the system at the dispose block.

10.2.3 The Case Study of a Do-It-Yourself Superstore For the analyses, the real data of a do-it-yourself superstore is used. In this store, generally five checkouts operate. Using the data provided by the checkout information system, the arrival rates for the different days and for the different parts of the days was estimated. For all periods, the Poisson arrival process is acceptable according to Kolmogorov-Smirnov tests. Based on Rényi’s limiting distribution theorem and its generalizations, the arrival processes of the two customer groups can also be approximated with Poisson processes (Rényi, 1956; Szántai, 1971a,b). The density function of the number of items bought by customers is also provided by the checkout information system. For describing it, a truncated geometric distribution with a mean of 3.089 is found acceptable by a chi-square test. As the service time of customers cannot be obtained from any information systems, it was measured manually. The relationship between the number of items bought and the service time was analyzed with regression analysis. A 0.777 correlation coefficient supported the assumption of linearity. According to the results of linear regression, service time has two parts. On the average, the part independent of the number of items bought lasts 0.5463 minute, reading a bar code needs 0.1622 minute. With linear regression, the standard deviation of these parameters and the service times of customers buying different amounts were determined as well (for details see Koltai et al, 2008). Results presented in this article are valid for a midday traffic intensity with an arrival rate most characteristic for the store (λ =95 customers/hour). According to the geometric distribution, customers buy generally only few items. Therefore, two of the 5 working checkouts was considered to be express servers (S=5, E=2). In the store in question, express lines have not been used yet. Therefore, the real queuing system could not be used to validate the simulation model. Consequently, the analytical models were used for checking the validity of results. The fundamental simplifications applied in analytical models were introduced to the simulation model. In the M/G/k simulation model, there is a common line for customers entitled to use express checkouts and another one for customers buying many items. In the M/G/1 simulation model, there are independent arrival processes for all of the checkouts and their own waiting lines. The analytical and simulation results gained by the same type of models are quite close to each other; accordingly, they can be considered valid (Table 10.1).

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Table 10.1 Analytical and simulation results Limit value Model

L=1

L=2

L=3

L=4

Analytical M/G/k Analytical M/G/1 Simulation M/G/k Simulation M/G/1

0.0492 0.3727 0.0481 0.3155

0.0417 0.2755 0.0431 0.2414

0.0811 0.3289 0.0838 0.3244

0.1563 0.4803 0.158 0.4882

10.3 Objective Functions for Operating Express Line Systems In time-based competition, the most important management objective in services is to decrease customer waiting. According to the classical objective of operations management, generally the average waiting time is minimized by service managers. With the help of queuing theory, measures related to the average waiting can easily be determined - and further on minimized. Our analyses showed, however, that as an effect of applying express checkouts, depending on the limit value, the average wait fluctuates in a high degree (Fig.10.2). With an erroneously determined limit value, not only the average waiting time but waits in express lines can be higher than in the original system. The application of express checkouts, as other specialization of servers, helps to make the services more standard. They do not necessarily reduce average waiting time but decrease the fluctuation in the length of services and, consequently, reduce the standard deviation of waiting time as well. It can happen that customers in an express line have to wait to the same amount as they would wait in a regular line but do not have to worry about that a customer buying huge amount will lengthen their waiting. Customers, being risk-averse, prefer (within limits) longer waiting with smaller fluctuations. The variance of waiting times can be determined with the statistical data of simulation or, in simple cases, with the help of queuing theory. The importance of reducing variance of waiting time attracts attention to the significance of human characteristics in service systems. According to the intention of perception management, instead of minimizing the average of objective waiting times the average of subjective waiting times should be reduced. The perceived waiting time is known only by the customer who passed through it. As people do not percept time linearly, there can be significant differences between the two values. The human time perception, according to the psychophysical literature, can be approximated by power functions (Stevens, 1957). To calculate perceived waiting times, after determining the values of some parameters, only the actual waiting times must be known. These values, however, can easily be determined by applying a suitable transformation. The evaluation of waiting depends on several factors. The same perceived waiting times can generate satisfaction to different degrees in different people. One of the main factors which determine customer satisfaction related to waiting is the value of the service for which people are waiting (Maister, 1985). Customers in express


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lines buy only few items, that is, they receive service of lower value. Accordingly, their satisfaction will be lower even if they must wait the same time as customers in the regular lines. The relationship between waiting and satisfaction can be described with a suitable utility function. For the calculations, as a simplification of the expected utility model, a mean-variance (or a two-moment) decision model can be used (Levy and Markowitz, 1979; Meyer, 1987). In this way, the transformation of waiting time into customer satisfaction, after determining the parameter values characteristic for customers, can be performed based on measures which can easily be determined analytically or empirically.

10.4 Optimization of the Waiting Process Actual waiting, perceived waiting, and satisfaction related to waiting constitute a simplified service-profit chain. Improving any of them will result in a higher service level. The ultimate management objective should be the maximization of customer satisfaction. To determine the customers’ satisfaction related to waiting, however, requires thorough knowledge about the customers and, consequently, timeconsuming and expensive analyses. The cost of this analysis may exceed the benefits which can be obtained by a system operated according to a more sophisticated objective function. Based on our analyses, it can be concluded, however, that there are no significant differences in the operation of an express line system whether it is operated according any of the first three objective functions. The numerical data for a case which is most characteristic for the superstore analyzed are given in Table 10.2. Table 10.2 The operation of the system with different objective functions and limit values Limit value Objective

L=1

Average waiting time 0.3403 Standard deviation of waiting times 0.7374 Average perceived waiting times 0.3288

L=2

L=3

L=4

0.257 0.5535 0.255

0.3125 0.5757 0.31

0.4614 0.7444 0.4491

In Table 10.2, the optimal objective function values are typed boldface. It can be seen that the same optimal limit value (L=2) is obtained independently of which objective function is used. This result has two consequences. First, managers trying to optimize the operation of their queuing systems can use, aside from satisfaction maximization, any of the possible objective functions and will get the same result (optimal limit value). Moreover in this way they will optimize (or at least improve) all of the measures mentioned.

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Second, as average waiting time can be optimized easily and fast with analytical models, there is no need for using a more time-consuming and hardly manageable simulation model. It must be mentioned that there are situations when the different objective functions determine different optimal limit values. Our analyses showed, however, that these limit values are numbers next to each other and, in these cases, the waiting measures are nearly equal independently of the applied limit values. Therefore, even if the different objective functions give different optimal solutions for the limit value, the different limits result only slight differences in the waiting measures.

10.5 Conclusions The application of express lines is a widely used management tool for waiting process improvement. One of the main parameters of express line systems is the limit value which controls checkout type selection. Its value must be selected carefully because introducing express lines with an improper limit value can increase customer waiting significantly. Therefore, determining the optimal limit value, which minimizes average waiting time, is one of the most important tasks of managers operating express lines. For determining optimal limit value, special tools are required. Our analyses show, however, that simple analytical models are accurate enough for practical applications. They give only rough approximation of operation and they are appropriate for analyzing only simple waiting measures and management objectives; however, they can be used to determine the optimal limit value. Using analytical models, the time, money and knowledge needed for developing and running simulation models can be saved. That is, analitical models provide an effective rapid modelling tool for service managers. It also must be mentioned, that beside limit value there is another parameter which can be used by managers for influencing waiting time without cost consequences. This is the ratio of express and regular checkouts (when the total number of checkouts is constant). With this parameter, if optimal limit values are used, waiting time cannot significantly decreased, therefore it is recommended to use this parameter to assure constant limit value when total number of checkouts is changed for some reasons. The waiting time decreasing effect of express lines are limited. Notwithstanding express lines are popular among customers. Therefore, to reveal all consequences of applying express lines, their effects on waiting distribution among the different customer groups and, accordingly, on satisfaction related to waiting times must be analyzed as well. These are topics of our further researches.


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References Hill A, Collier D, Froehle C, Goodale J, Metters R, Verma R (2002) Research opportunities in service process design. Journal of Operations Management 20(2):189– 202 Hillier F, Lieberman G (1995) Introduction to operations research. McGraw-Hill Koltai T, Kalló N, Lakatos L (2008) Optimization of express line performance: numerical examination and management considerations. Optimization and Engineering pp 1–20 Levy H, Markowitz H (1979) Approximating expected utility by a function of mean and variance. The American Economic Review 69(3):308–317 Maister D (1985) The psychology of waiting lines. In: Cziepel J, Solomon M, Surprenant C (eds) The Service Encounter, Lexington Books Meyer J (1987) Two-moment decision models and expected utility maximization. The American Economic Review 77(3):421–430 Rényi A (1956) A Poisson folyamat egy jellemzése (A possible characterization of the Poisson process). MTA Mat Kut Int Közl 1:519-527 Rothkopf M, Rech P (1987) Perspectives on queues: combining queues is not always beneficial. Operations Research 35(6):906–909 Stalk G (1988) Time–the next source of competitive advantage. Harvard Business Review 66(July-August):41–51 Stevens S (1957) On the psychological law. Psychological Review 64(3):153–181 Szántai T (1971a) On limiting distributions for the sums of random number of random variables concerning the rarefaction of recurrent process. Studia Scientiarum Mathematicarum Hungarica 6:443–452 Szántai T (1971b) On an invariance problem related to different rarefactions of recurrent processes. Studia Scientiarum Mathematicarum Hungarica 6:453–456

Chapter 11

Integrating Kanban Control with Advance Demand Information: Insights from an Analytical Model Ananth Krishnamurthy and Deng Ge

Abstract This paper investigates the benefits of integration of advance demand information (ADI) with the Kanban Control System (KCS). ADI shared by customers is integrated into production release policies thereby enabling simultaneous improvements in service levels and reductions in inventory and costs. Under Markovian assumptions, an exact analysis of the production system is carried out. Through numerical studies, the system performance is compared to those obtained from classical Kanban control system and base stock system with ADI.

11.1 Introduction Recent advances in information technology have led to the belief that sharing advance demand information (ADI) to manufacturers will allow customers to receive better service from their manufacturing suppliers. Manufacturers also expect that this ADI can be effectively integrated into their production inventory control systems (PICS) to reduce lead times and inventories. This paper investigates the effect of integrating ADI into Kanban Control Systems (KCS). Using analytical models, we quantify the improvements obtained in system performance when the KCS is integrated with ADI.

Ananth Krishnamurthy University of Wisconsin-Madison, Department of Industrial and Systems Engineering, 1513 University Avenue, Madison, WI 53706, USA, e-mail: [email protected] Deng Ge University of Wisconsin-Madison, Department of Industrial and Systems Engineering, 1513 University Avenue, Madison, WI 53706, USA, e-mail: [email protected]

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The effect of ADI on PICS has been the focus of several studies. Survey articles such as Uzsoy and Martin-Vega (1990) provide an overview of the prior research on kanban controlled systems. A number of researchers like PhiIipoom et al (1987) and Di Mascolo and Frein (1996) have studied various aspects of the design of a classical kanban controlled system. Other researchers have proposed and analyzed the performance of variations of the KCS. For instance, Dallery and Liberopoulos (2000) introduce the Extended Kanban Control System (EKCS). They show the EKCS is a combination of the classical KCS and the Base Stock (BS) system. They also show that the EKCS provides the flexibility to decouple design decisions related to production capacity and base stock levels. Buzacott and Shanthikumar (1993) introduces the Production Authorization Control (PAC) system that incorporates advance order information from customers. Karaesmen et al (2002) analyze a discrete-time make-to-stock queue and investigate the structure of the optimal policy and associated base stock levels. Liberopoulos and Koukoumialos (2005) analyze a system operating under KCS with ADI and conduct simulation experiments to investigate tradeoffs between base stock levels, number of kanbans and manufacturing lead times. The analytical model discussed here is a first step towards models that could provide understanding how system performance can be improved further by integration of the ADI with the kanban controlled system. The model presented in this paper is for a single-stage system. We compare system performance with that obtained under the classical KCS and BS system with ADI. Based on the Markov chain analysis, we show that the integration of the KCS with ADI results in superior system performance as the integration combines the best features of KCS and based stock systems with ADI. The remainder of the paper is organized as follows. Section 11.2 describes the operation of a system operating under the KCS with ADI, followed by Section 11.3 that describes the detailed Markov chain analysis for the system. Section 11.4 compares the performance of the different systems, and Section 11.5 summarizes the insights.

11.2 Kanban Control System with ADI This section describes the queuing network model of the KCS with ADI using the general framework provided in Liberopoulos and Tsikis (2003). The operational characteristics of the system are described in terms of movement of activated orders, products, and free kanbans in the network. The model is composed of a singlestage manufacturing station (MFG), fork/join synchronization stations (FJ1 , FJ2 ) and order delay station (OD). Figure 11.1 shows a schematic of the system. We assume that customer orders arrive at the system according to a Poisson process with rate λ . However, each customer places their order LTD time units in advance of the due date. We call LTD the demand lead time and let τd = E[LTD ] (the case of no ADI corresponds to the case where LTD = 0). Note that the demand lead time

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is customer specified and it is different from the planning lead time (LTS ) that the manufacturing system uses for planning order releases for production. Note that if sufficient ADI is available, the system might be able to meet customer demand with less finished goods inventory than that required in a system operating under the KCS without ADI. For instance, if E[LTD ] > LTS it is possible that the system operates in a make-to-order mode with minimal inventory. This paper focuses on the more interesting case wherein E[LTD ] < LTS . Consequently, orders received from customers are immediately activated. However, they may not be released into the manufacturing system immediately, as they might wait in buffer BD1 for a free kanban to be available in queue FK. When a free kanban is available in FK, an activated order in BD1 and a free kanban are matched together and released into the manufacturing stage MFG which consists of a single exponential server with mean service time μs−1 . After completing service, the product queues in the finished goods buffer FG. At buffer BD2 , LTD time units after an order is placed, the customer arrives demanding a product. If a unit is available in finished goods, the demand is immediately satisfied. The kanban attached to the order is released and routed back to FK where it is available to release another activated order into production.

K Kanbans FK

MFG

FG (Z) Satisfied Demands BD2

BD1

FJ1

Demands

τd

FJ2 OD

External Orders Fig. 11.1 Queueing network model of the KCS with ADI

We assume that (i) the number of kanbans, K in the system is fixed; (ii) demands that are not satisfied immediately get back-ordered; (iii) the system maintains a target base stock level, Z of finished products in FG. The factors affecting system performance are the demand and planning information, target base stock levels (Z), the number of kanbans (K), and the characteristics of the demand and manufacturing processes. The service times at the manufacturing station and the inter-arrival times of demands and orders are assumed to be independent. Since orders arrive at rate λ , and the service rate of the manufacturing station is μs , we assume that the system utilization is ρ = μλs ≤ 1.

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To analyze the dynamics of the system, we define the following performance measures at time t: C(t)= the number of kanbans/parts available at the manufacturing stage, F(t)= the number of free kanbans available at FK, P(t)= the number of pending orders waiting for free kanbans at BD1 , I(t)= the number of finished items in FG, W (t) =the number of waiting orders in OD, and B(t)= the number of backorders in BD2 . The dynamics of the KCS with ADI implies that the following flow conservation equations hold at any time t: F(t) + C(t) + I(t) = K P(t) + C(t) + I(t) = Z + W (t) + B(t)

(11.1) (11.2)

The main performance measures of interest are the (i) average work in process, E[C], (ii) average finished goods inventory, E[I], (iii) the probability of backorder, PB , (iv) the average number of backorders, E[B], and (v) the overall average total cost E[TC].

11.3 Markov Chain Analysis In this section, we analyze the Markov chain for the KCS with ADI. To develop the Markov chain analysis, we assume that the demand lead time LTD has an exponential distribution. Let X1 (t) = F(t) − P(t), X2 (t) = I(t) − B(t), t ≥ 0, then the system performance measures defined in Section 11.2 can be uniquely determined by states (X1 (t), X2 (t)) as follows: F(t) = X1+ (t), P(t) = (−X1 )+ (t), I(t) = X2+ (t), B(t) = (−X2 )+ (t), t ≥ 0 (11.3) C(t) = K − X1+(t) − X2+ (t), W (t) = K − Z − X1 (t) − (−X2)+ (t), t ≥ 0

(11.4)

where Xi+ (t) = max{Xi (t), 0},

i = 1, 2. Note that the size of Markov chain is infinite when no limits are imposed on the number of pending orders. To solve a finite Markov chain, we assume that the number of pending orders at BD1 is at most K0 , where K0 < ∞. Then, we have the following important properties for states: −K0 ≤ X1 (t) ≤ K − Z, t ≥ 0

(11.5)

−(K − Z + K0 ) ≤ X2 (t) ≤ K, t ≥ 0

(11.6)

The Markov chain for the system is developed as shown in Fig. 11.3. The state space can be partitioned into six areas based on the number of finished goods/backorders. Let Ni be the number of states in area i, where i ∈ (1, 2, 3, 4, 5, 6). Then we have the number of states in each area as follows, N1 = K0 + 1, N2 = 1 2 (2K0 + K − Z + 2)(T − 1), N3 = K0 + K − Z + 1, N4 = (K0 + K − Z + 1)(Z − 1), N5 = K0 + K − Z + 1, N6 = 12 (K0 + K − Z + 1)(K0 + K − Z). This implies that total number of states is N = ∑6i=1 Ni .


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Let π (x1 , x2 ) be the limiting probability i.e. P {limt→∞ [X1 (t), X2 (t)]} = π (x1 , x2 ), where −K0 ≤ x1 ≤ K −Z, −(K0 +K −Z) ≤ x2 ≤ K. Let T = K −Z, we can write the Chapman-Kolmogorov equations for each of the six areas of the Markov chain. As an example the equations for Area 6 where −(T + K0 ) ≤ x2 ≤ −1, −K0 ≤ x1 ≤ T − 1 are given below: For x2 = −(T + K0 ), x1 = x2 + T :

μπ (x1 , x2 ) = (T − x1 + x2 + 1)τd−1 π (x1 , x2 + 1)

Area 1

0, K Tα

(T − 1)α

Tα

μ

λ

···

λ

−K0 , K

(T + K0 )α

μ −1, K − 1

μ (T + 1)α

λ

··· ···

μ

λ

−K0 , K − 1

(T + K0 )α

μ

μ

... · · · ... ... · · · ... .. .. · · · .. .. . . . . 2α μ (T + 2)α μ μ (T + 1)α ··· λ λ λ λ T − 1, Z + 1 0, Z + 1 −1, Z + 1 −K0 , Z + 1 ··· ··· α 2α (T + 1)α (T + K )α μ Tα μ μ μ · · · Area 3 λ λ λ T, Z T − 1, Z −K0 , Z 0, Z ··· −1, Z ··· μ α μ μ · · · μ T α μ (T + 1)α (T + K )α μ λ λ λ λ λ T, Z − 1 1, Z − 1 0, Z − 1 −K0 , Z − 1 ··· ··· (T − 1)α · · · μ Tα (T + K )α · · · μ μ μ ... · · · ... ... ... ... Area 4 ··· ··· ··· ··· Area 2

...

0, K − 1

λ

−1, K

(T + 1)α

μ λ

1, K − 1

λ

(11.7)

0

0

0

α

μ T, 1

Area 5

λ μ

2α

μ

T − 1, 1 α

μ

T, 0 μ

Area 6

λ

λ

··· 2α · · ·

λ

μ

(T + 1)α

λ

0, 1 λ

Tα

μ

μ

μ

(T + 2)α

−1, 1

λ μ

(T + 1)α

λ −1, 0 0, 0 ··· μ μ α ··· Tα λ λ 0, −1 −1, −1 ··· T − 1, −1 (T − 1)α · · · Tα μ ... · · · ... ··· T − 1, 0

μ

α

λ

···

(T + K0 )α

λ

λ

μ

· · · −K0, 0 · · · μ (T + K )α · · · λ −K0, −1 (T + K − 1)α ··· ... · · · ... 0

μ

···

−(K0 − 1), −(T + K0 − 1)

−K0 , 1

0

2α

μ λ

−K0 , −(T + K0 − 1)

μ

α −K0 , −(T + K0 )

Fig. 11.2 Markov chain transition diagram for the EKCS with ADI, where α = τd−1

For x1 = x2 + T : (λ + μ )π (x1 , x2 ) = μπ (x1 − 1, x2 − 1) + (T − x1 + x2 + 1)τd−1 π (x1 , x2 + 1) (11.8)

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For x1 = −K0 : (T − x1 + x2 )τd−1 + μ }π (x1, x2 ) = λ π (x1 − 1, x2 )+ (T − x1 + x2 + 1)τd−1 π (x1 , x2 + 1) (11.9) For −K0 < x1 < x2 + T : {λ + (T − x1 + x2 )τd−1 + μ }π (x1, x2 ) = λ π (x1 − 1, x2) + μπ (x1, x2 − 1) + (T − x1 + x2 + 1)τd−1 π (x1 , x2 + 1)(11.10) These balance equations can be solved to obtain the key performance measures. However, the expressions for the performance measures of KCS with ADI are not closed form. Let Pb , E[I], E[B], E[C] be the probability of being backordered, and the expectation of I(t), B(t),C(t), respectively. Then, if ρ = μλs and τd = E[LTD ], we have: Pb =

∑

π (x1 , x2 )

(11.11)

∑

x2 π (x1 , x2 )

(11.12)

∑

|x2 |π (x1 , x2 )

(11.13)

(x1 ,x2 ):x2 0

E[B] =

(x1 ,x2 ):x2 0

+ (K − x+ 1 − x2 )π (x1 , x2 )

(11.14)

11.4 System Comparison Since a system operating under KCS with ADI combines features of both the classical KCS and BS system with ADI, we compare the performance of all three policies assuming that the manufacturing system has same configuration and the parameters characterizing the ADI and demand arrival processes are the same. Note that analytical expressions have already been established for the performance measures of KCS and BS with ADI systems by Dallery and Liberopoulos (2000) and Karaesmen et al (2002) respectively. Table 11.1 shows expressions of performance measures for these two systems. To compare system performance under all three control policies, we introduce the expected total cost defined in Equation 11.15, where hw , h f and b are cost rates for average work in process, finished goods and backorders, respectively. E[TC] = hw E[C] + h f E[I] + bE[B]

(11.15)


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Table 11.1 Analytical Expressions for Performance Measures Measures

BS with Deterministic ADI

Classical KCS

Pb

ρ K+1

E[I]

e−μτd (1−ρ ) ρ Z+1 Z + λ τd − 1−ρ ρ 1 − ρ Z e−μτd (1−ρ )

E[B]

ρ K+1 1−ρ

e−μτd (1−ρ ) ρ1−ρ

E[C]

ρ (1−ρ )

ρ (1−ρ K ) (1−ρ )

K − 1−ρ ρ (1 − ρ K ) Z+1

11.4.1 Design of Experiments This section presents the design of experiments used for comparing the performance of the KCS with ADI with the classical KCS and BS system with ADI. In these experiments, the service time of the manufacturing station is assumed to have an exponential distribution with mean μs−1 = 1. The experiments are conducted by varying K = (5, 10, 20, 30), Z = (0, K/2, K) and λ = (0.5, 0.6, 0.7, 0.8, 0.9), respectively. We assume that the average demand lead time LTD (τd ) is set as τd = 0.9τs , where τs , the average flow time (the average time from order activation at BD1 till the delivery of a finished product to FG is estimated by τs μs 1−λ . Here we set K0 large enough so that the underlying Markov chain is finite, and yet no more than 0.1% of the orders that arrive are rejected from the system.

11.4.2 Effect of Base Stock Levels on the Performance Measures In this section, we discuss the effect of base stock level Z on the performance measures for the three different policies. The experiment was carried on λ ∈ {0.5, 0.6, 0.7, 0.8, 0.9} and K ∈ {5, 10, 20, 30}. For each given (λ , K), Z ranges from 0 to K. We compare E[B], E[I] and E[TC] for KCS with ADI, BS with ADI and the classical kanban system (KCS). Figure 11.3 plots the trade-offs obtained. In particular, Figures 11.3 i-a and i-b show that the average finished goods of the system operating under KCS with ADI is less than that of system operating under BS with ADI or the classical Kanban system. i.e., E[I] ≤ min(E[Ik ], E[Ibsa ]). This implies that KCS with ADI provides a better control over inventory than the base stock system with ADI or the classical KCS. Figures 11.3 ii-a and ii-b show that as Z increases, the average number of backorders decreases for both the KCS with ADI and BS with ADI, but is constant for the KCS. This is because both KCS with ADI and BS with ADI use a target stock level Z to reduce the backorders. The KCS does not set a base stock level, and hence the number of backorders in the system is constant for a given number of kanbans,

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K. We also notice that the average number backorders of the system operating under KCS with ADI lies between those of BS with ADI and classical KCS. Figures 11.3 iii-a and iii-b show the tradeoffs with respect to total cost. We notice that for a system operating under KCS with ADI, the E[TC] function is neither convex nor concave over Z. However, for the BS system with ADI, the expected total cost is convex over Z. As expected, for the KCS the cost is constant, for a given K and λ . For low values of λ (or system load), the KCS with ADI behaves similar to the BS with ADI, but for high values of λ (or system load), the KCS with ADI achieves lower cost than BS with ADI for all values of Z.

Fig. 11.3 Effect of Z on Performance Measures

11.4.3 Effect of Number of Kanbans on the Performance Measures In this section, we study the effect of number of kanbans on the performance measures for the KCS with ADI, BS with ADI and the classical KCS. The target base stock level Z is set as Z ∗ , which is the optimal base stock level for BS with ADI hf ln h +b

system, where Z ∗ = varied from Z ∗ to 30.

f

lnρ

ρ) + μτdln(1− (Buzacott and Shanthikumar, 1993) and K is ρ


139

Figure 11.4 plots the performance tradeoffs. In Figures 11.4 i-a and i-b, we see that for a system operating under the KCS, E[I] increases almost linearly as K increases, but for the KCS with ADI, E[I] increases initially with the increase in K, but is then bounded by the target stock level Z ∗ . This is due to the structure of the KCS system with ADI: the excess of kanbans queue up as free kanbans waiting for activated orders. This prevents release of additional kanbans into production limiting the built up of excess finished goods inventory. Figures 11.4 ii-a and ii-b show that initially E[B] decreases with increase in K, but then approaches a constant as E[I] approaches the target base stock level. The reason is similar to that given above: when E[I] approaches the target stock level, increase in K does not reduce backorders, as the additional kanbans queue up as free kanbans instead of being used to further reduce backorders. In Figures 11.4 iii-a and iii-b, we see that for a system operating under KCS, the expected total system cost, E[TC] is convex, but for a system operating under KCS with ADI, the expected total cost is neither convex nor concave. The optimal number of kanbans for the KCS with ADI appears to be close to the optimal kanban setting for the classical KCS. For either low or high λ (system load), the KCS with ADI always performs better than classical KCS.

Fig. 11.4 Effect of K on Performance Measures

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11.4.4 Effect of Pair (K, Z) on Total Cost This section demonstrates the impact of control pair (K, Z) on the overall performance. We vary K from 1 to 30 and Z from 0 to K. For each λ ∈ {0.7, 0.8, 0.9}, we consider all 495 combinations of (K, Z) and study its impact on the total cost. Figure 11.5 shows the case of λ = 0.9. As we have seen in Fig. 11.3 iii-b and Fig. 11.4 iii-b, E[TC] does not demonstrate convexity or concavity over the control pair, and E[TC] has local minimums.

Fig. 11.5 Effect of (K, Z) on Total Cost

11.5 Conclusions and Ongoing Work This paper provides analysis of single-stage single-class production-inventory Kanban control system with ADI. We develop an analytical model for a system operating undet the KCS with ADI and compare the performance to system operating under the BS system with ADI and the classical KCS. Our results show that the KCS with ADI helps to reduce the inventory levels and backorders beyond that possible in the KCS or BS with ADI for the same system parameters. However, cost function for the KCS with ADI is neither convex nor concave, so determining optimal system parameters for a system operating under KCS with ADI is a challenge. Our ongoing


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work is aimed at developing detailed closed form approximations for key performance measures and optimizing overall system performance over the controllable parameters.

References Buzacott J, Shanthikumar J (1993) Stochastic models of manufacturing systems. Prentice Hall, New Jersey Dallery Y, Liberopoulos G (2000) Extended kanban control system: Combining kanban and base stock. IIE Transactions 32(4):369 – 386 Di Mascolo M, Frein Y (1996) An analytical method for performance evaluation of Kanban... Operations Research 44(1):50 – Frein Y, di Mascolo M, Dallery Y (1995) On the design of generalized kanban control systems. International Journal of Operations & Production Management 15(9):158 – 184 Karaesmen F, Buzacott JA, Dallery Y (2002) Integrating advance order information in make-to-stock production systems. IIE Transactions 34(8):649 – 662 Liberopoulos G, Koukoumialos S (2005) Tradeoffs between base stock levels, numbers of kanbans, and planned supply lead times in production/inventory systems with advance demand information. International Journal of Production Economics 96(2):213 – 232 Liberopoulos G, Tsikis I (2003) Unified modelling framework of multistage production-inventory control policies with lot sizing and advance demand information. In: Shanthikumar J, Yao D, Zijm W (eds) Stochastic Modeling and Optimization of Manufacturing Systems and Supply Chain, Kluwer Academic Publishers, pp 271–297 PhiIipoom PR, Rees LP, Tailor III BW, Huang PY (1987) An investigation of the factors influencing the number of Kanbans required in the implementation of the JIT technique with Kanbans. International Journal of Production Research 25(3):457–472 Uzsoy R, Martin-Vega L (1990) Modelling Kanban-Based Demand-Pull Systems: A Survey and Critique. Manufacturing Review 3(3):155–160

Chapter 12

Rapid Modelling in Manufacturing System Design Using Domain Specific Simulators Doug Love and Peter Ball

Abstract Simulation is an important tool for evaluating manufacturing system designs in the face of uncertainties like demand variation, supply variation, breakdowns and absenteeism. The simulation model building and experimentation stages can be long when compared to the time available for the overall manufacturing system design leading to potential benefits of simulation being limited. Thus the simulation process may be iterative for a single model/design but rarely iterates across multiple models for new design options. In order to maximise the value of simulation and to improve the design outcome the model building time needs to be minimised to keep pace with the manufacturing system design process. This paper argues that problem specific interfaces are needed for simulators to allow rapid and intuitive model creation. This paper reviews two case studies that illustrate an approach using domain-specific simulators combined with specialist software that manipulates the design data into the form required by the modelling system. The preprocessor-based simulators were developed to avoid the user having to specify any of the simulation logic which speeds up model building considerably. This paper contributes to the rapid modelling field by showing how domain specific, data driven simulators can enhance the manufacturing system design process.

12.1 Simulation in Manufacturing System Design Many of the key performance aspects of a manufacturing system are related to the effect of stochastic events on its operation and although mathematical modelling can Doug Love Aston Business School, Aston University, Birmingham, B4 7ET, U.K., e-mail: [email protected] Peter Ball Department of Manufacturing, Cranfield University, Cranfield, Bedford, MK43 0AL, U.K., e-mail: [email protected]

143

144

Doug Love and Peter Ball

help with some of these it is simulation that provides the most flexible and powerful means of estimating their impact. Reliable estimates of lead times, work in progress levels, delivery performance, resource utilization etc. all depend on proper representation of such sources of uncertainty. Determination of the robustness of the design requires study of external and internal sources of uncertainty, for example changes in volume and product mix are external to the system whilst breakdowns or scrap are internal factors. Smith (2003) reviews the literature on the use of simulation in manufacturing and lists many examples of its use in the design of manufacturing systems. However the review finds few papers that are concerned with role of simulation in a comprehensive manufacturing system design (MSD) process such as that proposed by Parnaby (1979). Kamrani et al (1998) presented a simplistic three stage methodology for cell design in which simulation was the third phase. Other examples of simulation being discussed in the context of the manufacturing system design process include Paquet and Lin (2003) who introduce ergonomic considerations and AlDurgham and Barghash (2008) who propose a framework for manufacturing simulation that covers some aspects of the design problem but is presented from a more general perspective. Conventionally simulation has been linked with the ’dynamic design’ stage of the manufacturing system design process which follows the concept and detail design phases in which steady-state conditions are assumed (Love, 1996). During these earlier stages average losses or utilization factors are assumed to cover internal uncertainties and average conditions said to apply to demand and product mix. Only at the dynamic design stage are these factors studied (and represented) in more depth so that reliable estimates of many of the manufacturing system’s key performance metrics will only be revealed at this late stage. Ideally the evaluation of dynamic performance of the manufacturing system should be included in every stage in the design process but this means that the simulation model would need to change as the engineers develop their view of the manufacturing system design. Lewis (1995) proposed a manufacturing system design methodology that incorporated just such a synchronized approach but it was never fully implemented. He suggested that the simulation model should be used throughout the system design and through the all the iterations of its development. The feasibility of such an approach clearly depends on ability of the modeller to complete the simulation re-build loop inside the time available for each stage in the system design process. If that cannot be done then inevitably the simulation will be left until the system design has stabilized to the point where major changes in the simulation model would not be needed - that is why the simulation is often built toward the end of the design project once the detail design phase is complete. Of course it means that any serious deficiencies in the design that emerge from the dynamic analysis may require expensive revision of the system architecture that could have been accommodated more easily at an earlier stage. Manufacturing system redesign is normally initiated when there is a compelling business need and that need is usually time-sensitive so that there is considerable pressure to complete the project as soon as possible. This pressure means that design team are unlikely to

Title Suppressed Due to Excessive Length

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favour extending the project time scale even if the extra time spent on a simulation study would result in a higher quality and more robust design. Clearly if the time required to perform the simulation analysis could be significantly reduced then it would alter the trade-off between design quality and project duration in favour of the use of simulation.

12.2 Rapid Modelling in Manufacturing Systems Design During the early stages in MSD the architecture of the system may change substantially, for example the cell and related part families may be redefined completely, so simulation support through this phase implies an ability to completely rebuild the simulation model quickly. As the architecture is developed a series of models will be required to test out very different alternatives. Differences will not merely relate to number and distribution of resources but may require more fundamental revisions to reflect changes to cell families, material flow paths, work and skill patterns and machine tool capabilities. This means that the time to build a complete model from scratch is a key determinant of whether simulation can be used to support this early phase in the project. Building a model from scratch always takes a significant period of time, especially if the model is complex Cochran et al (1995) suggest that over 45% of simulation projects take more than three months and nearly 30% require over three man-months of effort. We have not been able to identify a more recent study that assessed the impact of the technical enhancements seen since that time or was focused specifically on manufacturing design projects. Speeding up model building has long been a desirable objective for simulation system developers, for example see Love and Bridge (1988). It is clear that whilst improvements have been made, the position is still seen as one in which scope exists for further improvement. For example Pedgen’s review (see Pegden, 2005) of future developments in simulation states that: “If we want to close the application gap we need to make significant improvements in the model building process to support the fast-paced decision making environment decision making environment of the future”. In response to this pressure software systems have improved considerably, notably in relation to the use of graphics and reusable elements; for examples of this trend see the Simul8, Witness and Arena systems amongst others. These developments focus on speeding up the translation of the model logic into executable code whilst other enhancements provide support for multiple runs, statistical analysis and the production of common reports, graphs etc. that help by speeding up the experimental process. However the domain independence or breadth of these systems means that the user is still required to provide much of the detail logic of the model. This is likely to be a significant task Robinson (2004) suggests the conceptual modelling stage takes around one third of the total simulation project time. Thus, although these improvements could be expected to speed up model development to some extent, they are limited by primarily addressing the coding and experi-

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mentation parts of the simulation model development cycle leaving the conceptual modelling phase relatively untouched. Whilst the need to repeat the conceptual modelling stage is clearly a serious inhibitor on the use of such systems in the architecture design of the manufacturing system it is a less significant issue for refinement and detail design. The refinement stages of the manufacturing system design process will generate a need for modifications to an existing model even if the underlying conceptual simulation model remains largely unchanged. The ease and speed with which these can be done will have been aided by the improvements mentioned above but may still require longer than the engineer would wish. The length of the minor modify-experiment cycle may depend on the ease with which the engineer can interact with the model to implement the required changes and perform the necessary experiments and that, in turn, may depend on the nature of the simulation software. It could be argued that some simulation systems already allow models to be built using only data without any programming and some simulation software companies may argue that their interfaces are intuitive and can be learnt very quickly. But this would not be a view shared by a typical manufacturing engineer unfamiliar with simulation interfaces or the subtle tricks needed to get the systems to represent the logic required with recourse to programming. Ball and Love (1994) point out that interfaces may make simulation packages easier to use but this does not necessary mean easy to use, i.e. easy to use describes the simplicity by which the user can create the model from data from the problem domain. Data-driven simulators are usually defined as systems that allow a user to create a running model without the need to do any programming, for example see Pidd’s definition (Pidd, 1992). Configuration options are used to define or modify the operational logic of the model usually through menus choices and the setting of entity properties. Although it is true that this approach does use ‘data’ to define the model, it may still require the user make decisions that are normally associated with conceptual modelling, for example to define model inputs, outputs, and data requirements and to decide what components are to be included and the level of detail with which they will be represented. The more freedom the system offers to the user the wider its potential range of applications will be, but the more specialist knowledge will be needed to use it. O’Keefe and Haddock (1991) present a useful diagram that demonstrates the continuum from pure programming languages through the type of system described above to highly focused problem-specific simulators that merely require data population. The approach used in the cases described here is close to the problem specific end of the range; the ‘model’ is pre-built and the options offered are limited to those that are directly related to the manufacturing system design problem itself. They would be recognised by an engineer as part of the normal specification of the design and are expressed in domain specific language. The conceptual modelling decisions have already been made and are hard-wired into the system. The model is populated by the data that is loaded into it; in these cases the data describe the products, production processes and resources that make up the real system. Normally this data will be extracted from the company databases or ERP systems and formatted be-


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fore uploading although Randell and Bolmsjö (2001) built a demonstration factory simulation that showed it was: “feasible to run a simulation using the production planning data as the only information source”. The data used for this project are very similar to those required by SwiftSim (Love, 2009) - see below. Detailed configuration options may still be required but they are defined and presented in a form and language familiar to the engineer using a problem specific interface. This means there is no need for users to learn specialist simulation concepts and terminology. Of course other aspects of the simulation art are still required, especially those related to the experimentation. The avoidance of the conceptual modelling stage altogether and the fact that the coding stage is also eliminated means that the user can move from data gathering to running model very quickly since data upload and parameter and option setting are all that are required to create a running model. The Robinson (2004) suggestion that the project time is roughly split evenly between conceptual modelling, coding and experimentation (he excludes implementation from this) means that use of this type of data-driven simulator could save up to two thirds of the simulation project time. This paper reviews two case studies that illustrate this approach.

12.3 Case Applications 12.3.1 Case Study 1 Cell Design in an Aerospace Company The aerospace case is an example of the use of a data-driven simulator in the design of a cellular manufacturing system. This company manufactures complex parts for the aerospace industry with application in both the military and commercial markets and their customers include all the major manufacturers of aircraft. Moulding and related processes are used in their manufacture so that this application was slightly unusual in that the processes were very different from those seen in a conventional machine shop. The variety of parts in the cell’s product family was also substantial - around 3200 part numbers were considered ‘live’ and each part passed through around 10 operations. The number of work centres in the cell was more modest at around 70 although many contained multiple stations. At some stations individual parts were loaded and processed by the operator whilst at others parts were loaded in bulk and the processing took place unattended. The need to changeover might be triggered by a change in part number from one batch to the next or by a change in some other property or attribute of the part. Operators were multi-skilled and those skills differed from person to person and shift working was the norm. Special tooling was used extensively and in some cases travelled with the work through several operations and could be considered an important resource limitation. In some cases parts were assembled together at certain operations so that the process route data had to include bill of materials information. In some cases the constituent parts were made in the same cell whilst in other instances they were produced elsewhere. MRP

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generated works orders were to be used by the company to drive the production programme for the cell. The design team recognised the potential benefit of using simulation but were concerned that it would take too long to develop a usable model given the tight timeframe that they had been given for the project. The complexity of their processes and the size of the part family were also seen as likely to extend the development time needed for the model. On the other hand the ability to test the robustness of the design was recognised as especially important for high-variety cells where shifts in product mix can cause unforeseen problems in sustaining delivery performance and utilisation levels. Since the redesign involved reorganisation of existing facilities rather than the introduction of new processes it followed that much of the data held in the company’s ERP system could be used to populate the simulation model. A revised version of an existing data-driven batch manufacturing simulator had recently become available at Aston University so it was decided to use that package for the project. The original system (ATOMS, Bridge see 1991) had employed a manual user-interface in which the engineer typed in all the relevant data and, whilst some basic data could be uploaded from files, extensive manual editing was always required before a viable model could be generated. Although the core of the system was little changed the revised facilities meant much larger models could be run and a more comprehensive range of upload options were implemented through a spreadsheet interface. These developments meant that ERP data could be used without simplification to generate the model. SwiftSim (Love, 2009) relies entirely on the base manufacturing data and a range of configuration options (that are also defined by the uploaded data) to generate a running model of a manufacturing system. The data required is extensive but is no more comprehensive than would be needed to specify the manufacturing system design. The system does not offer any programming options at all - if the required functionality is not present then it cannot be added. To ensure that its range of functionality was as comprehensive as possible the original design was based on a study of cell design practise across a UK-based multi-national company. Engineers from the company’s design task forces located in plants across the country were interviewed to identify the features that the system needed to offer. The system was also refined by application in a number of in-house redesign projects. Domain data are used to create the model directly, i.e. the data are formatted, uploaded (or manually entered into the system), run options selected and the model then executes immediately. The user defines materials (i.e. part numbers), process routes, bills of materials, work stations, work centres, operators, work patterns, skill groups, control systems (MRP, Kanban), sequencing rules (FIFO, batching etc), stock policies, suppliers and lead times, demand sources (generated or input) etc.. The model is created directly from this data. Company terminology is used throughout so, for example, actual part numbers are used and operators are given their real names. The system can generate a range of standard reports that vary in the level of detail offered from simple tables of resource utilisation to event log files that record everything that happened in a run. The original ATOMS system provided a limited graphical, schematic, representation of the simulated system that could be used for


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debugging and diagnostic investigation. For this type of system the graphical display of the system status is rarely used when performing experimental runs but it remains very useful for diagnostics so that aspect will be a core focus of the new graphical extension currently being considered for SwiftSim. The concern to ensure the model was built as quickly as possible and the fact that the company had no experience of the modelling system influenced their decision to employ an external consultant (one of the authors) who had knowledge of both the manufacturing design process and the simulator. This meant that there was a learning curve faced by the consultant in becoming familiar with the companys products, processes etc. This approach ensured that the first model was produced quickly but the extra communications involved did slow the iteration cycle down during later stages in the project. The raw process and sales demand data were extracted from the company’s ERP system into spreadsheets where they could be readily reformatted for upload. The data for work stations, operators, materials, process routes (including bills of material) were all handled that way. Generating demand data proved to be a little more complex as an MRP calculation was performed in the spreadsheet to convert product demand to that for the cell family parts. This had the advantage of avoiding any distortions that might have been present in a works order history extracted from ERP. The disadvantage was that the spreadsheet calculation was slow, taking 6-8 hours on average. The absence of a programming capability did not prove to be a constraint as the simulator handled all the complications of the manufacturing processes without the need for any special ‘tricks’ or deviations. The time the system needs to create a model from a spreadsheet is very short (less than a minute) and run times are also reasonable taking around an hour to run a year’s simulated operation of the cell. However the time required for initial familiarisation and analysis, data extraction and reprocessing and data validation and correction meant that the first proper model took around 100 man hours to produce including the time needed to include program the MRP explosion into the spreadsheet. This time also included the consultants learning curve of around 20 hours that would have been avoided by a SwiftSim-trained engineer. Subsequent revisions to reflect design changes or different performance requirements could be accommodated much more quickly taking around 8 man hours to revise the data set, upload and perform a test run. These times are taken from contemporaneous log of the projects task times that was used to track progress and resources used. Once the base model had been created the engineers were able to obtain feedback on design changes quite rapidly although this cycle time would have been reduced and some of the initial creation problems may have been avoided if the engineers had used the simulator themselves from the beginning of the project. The engineers were able to use the standard reports from the system and generally they provided the information needed although the ability to show an animated graphic of the cell running was seen as very desirable, especially for communicating with both senior management and the shop floor.

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12.3.2 Case Study 2 High Volume Production Line Design The second case study is drawn from a high volume, engineered product environment. The company regularly introduces new products which trigger the development of new production lines. A production line is developed iteratively over a number of months and simulation is used as standard practice within those iterations. There are many individuals involved in the production line design process and although many regularly use simulation only a few are considered simulation experts. The focus of the design activity is the production line, with some links to the support, supply chain, etc. activities. The initial users of the simulation output are the wider design team to trigger redesign work or to confirm performance. The final simulation output is used as part of the senior management sign off process. The role of simulation in this case is to support the activities of the manufacturing engineers in removing risk from the design process and, importantly, triggering design changes that would typically result in a 10% performance improvement. Numerous simulation models are created during the design of a production line resulting from changes to numbers of machines, machine cycle times, process quality, expected output rates, etc. The models include details of buffers, selection rules, conditional routings, scrap rates and operator behaviour. Given their size (100 entities in a model is not unusual) and the scope of the potential changes, the models are rapidly rebuilt from scratch each time rather than modifying a base model. This rapid rebuilding of models is considered more robust than model modification and the scope of the changes required mean that such modifications could take longer than is available to the overall design team. The rapid building of simulation models is achieved through a tailored spreadsheet interface to a commercially available simulation package. The users work with the interface to specify the model through either manual entry or copy and pasting data from other design spreadsheets. The data entered represents the entities to be modelled as well as the control parameters. Populating the interface the first time for a new production line design typically takes several days, however, once achieved subsequent design changes can be accommodated easily with a day, often in hours. The early modelling work takes many days as the first models are run are deterministic and stochastic enhancements are progressively added and experiments performed. Once set up, the interface is able to build the model in the simulation package, run the model a number of times and retrieve the results. The interface contains only sufficient functionality to build models for that particular company. Therefore the user works within the user interface using terminology of a manufacturing engineer rather than generalised simulation terminology and is restricted to entering data typical of that companys requirements. The overall time from start to finish of modelling a given line is of the order of weeks. Relatively therefore the model build and run time is short for a given scenario. Overall modelling effort is actually dictated by the design iterations creating new scenarios. Manufacturing engineers use the simulation interface to build and run simulation models, sometimes with the guidance of the simulation experts. The company specific functionality of the simulation interface means that data specified in the inter-


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face that completely defines the model creation and execution is readily understood by all, whether or not they were part of initial modelling work. This contrasts with the typical view that simulation models built by others take time to fully understand. The size of the models means that manual creation of both the model logic and the graphical display would take a significant amount of time to create; potentially the speed is such that modifications would be triggered by the manufacturing engineers before the model was completed. Experimentation times are typically of the order of hours, sometimes scenarios are batched together and run overnight to use otherwise idle computers. The modelling approach therefore uses the power of a commercial simulator to model complex and varied systems and combines this with the simplicity of an interface dedicated to the particular companys work. This separation of the model creation from the power of the simulation software enables staff to quickly create models without having to develop a dedicated simulator or use significant staff time. In summary, the approach combines the power of a commercial simulation package with the speed and ease of use of a dedicated spreadsheet based interface in the language of the manufacturing engineer and allows rapid creation of models for experimentation by simulation experts and non-experts alike. The speed of the modelling is within the pace of the wider design team activity and genuinely informs the design process triggering design iterations and confirmation of performance before sign off.

12.4 Discussion of the Cases The paper has argued that the traditional relationship between manufacturing system design and simulation needs to evolve to truly draw on the benefits of simulation as an integral part of the dynamic design stage. The discussion went further to make the case that the dynamic design should be iterative starting at the concept stage and that to enable this to take place the interface to simulation systems should be in the language of the manufacturing engineers who are making the critical design decisions. The paper has presented two different cases where simulation models have built to directly contribute to the manufacturing system design process. The following discussion reviews how far these cases go towards enhancing the design outcome. Both cases address the integration of simulation into the manufacturing system design process. The cases demonstrate the influence of simulation on the design outcome as well as confirming performance. In both cases there was a simulation expert supporting the design activities and notably in case two those manufacturing engineers who are in the core of the design team are also users of the simulation system. The cases show the use of simulation to improve design performance, however, its influence on the concept design differs according to the point at it is deployed at the design stage. Whilst the first case demonstrated the influence on the design con-

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cepts in the second case simulation was utilised after the production line concepts emerged and therefore its role was to improve the performance of a given design option. Design iterations can vary in magnitude from parameter changes (such as cycle times and material control rules) to more fundamental structural changes (such as number of machines and routings). In case two most iterations were parameter changes however there were occasional more fundamental changes that resulted, as would be expected, in longer model creation times. Developments in simulators have potential to improve simulation model build times and in turn influence its role in manufacturing systems design. The development of a domain specific simulator requires both simulation and application domain knowledge. Two different approaches were illustrated the case two company used a standard commercial simulation system as the basis of their simulator whereas SwiftSim was developed through an academic research project with industrial collaborators. Interestingly the developments most valuable to these cases were core functionality improvements rather than those relating to animation. The role of the manufacturing engineer in the use of simulation varies in these cases. Case one was lead by the simulation expert where as case two was supported by the simulation expert. It has to be noted that simulation experts were used when subtle ‘tricks’ are required that are not a standard part of the interface functionality. A simulation specialist may be used to interface between the engineer and the model but this approach also has drawbacks. The specialist translates the engineer’s requirements into a model suitable for the purpose but the risk is that features are lost in translation and delays result. It may be that the popularity, mentioned earlier, of simple spreadsheet models with manufacturing engineers reflects a desire to directly control all aspects of the analysis. The level of data translation required from the manufacturing engineering design world into the simulation analysis world and back influences the level of robustness of the analysis process as well as the time taken to complete it. Both cases feature a minimum level of translation of data from the manufacturing engineers world to the simulation world, hence the manufacturing engineer could readily understand the model construction and outputs. Subsequently this minimises any nervousness with verification. Both cases present implications for model build time and indicate that they are built rapidly when compared to typically quoted figures from the literature. The rapid model building has had two impacts: firstly, the simulation output was influencing the design outcome rather than just confirming performance and, secondly, the level of detail possible is very high providing greater confidence in the design outcome.

12.5 Conclusions This paper has presented a discussion on the relationship between the manufacturing system design process and the simulation modelling process. It was argued that


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to improve the design outcome, the model building process needs to be reduced significantly to enable the results of simulation to truly influence the selection and refinement of design concepts. The detail of the two industrial cases demonstrates the challenges for simulation use as well as the benefits obtained. From this, key issues of integration of simulation, the influence on concept design, the functionality of commercial simulators, the role of the manufacturing engineer and data translation were identified and discussed. Overall the paper has demonstrated how domain specific, data driven simulators can enhance the manufacturing system design process.

References AlDurgham MM, Barghash MA (2008) A generalised framework for simulationbased decision support for manufacturing. Production Planning & Control 19(5):518 – 534 Ball PD, Love DM (1994) Expanding the capabilities of manufacturing simulators through the application of object-oriented principles. Journal of Manufacturing Systems (6):412–442 Bridge K (1991) The application of computerised modelling techniques in manufacturing system design. PhD thesis, Aston University Cochran JK, Mackulak GT, Savory PA (1995) Simulation Project Characteristics in Industrial Settings. Interfaces 25(4):104 – 113 Kamrani A, Hubbard K, Parsaei H, Leep H (1998) Simulation-based methodology for machine cell design. Computers & Industrial Engineering 34(1):173–188, cellular manufacturing systems:Design, Analysis and Implementation Lewis P (1995) A systemic approach to the design of cellular manufacturing systems. PhD thesis, Aston University Love D (1996) The design of manufacturing systems. In: International Encyclopaedia of Business and Management V4, Thompson Business Press, pp 3154–3174 Love D (2009) SwiftSim overview. URL http://oimabs.aston.ac.uk/swiftsim Love DM, Bridge K (1988) Specification of a computer simulator to support the manufacturing system design process. In: Proceedings International Conference Computer-Aided Production Engineering, SME, Michigan O’Keefe RM, Haddock J (1991) Data-driven Generic Simulators for Flexible Manufacturing Systems. International Journal of Production Research 29(9):1795– 1810 Paquet V, Lin L (2003) An integrated methodology for manufacturing systems design using manual and computer simulation. Human Factors and Ergonomics in Manufacturing 13(1):19–40 Parnaby J (1979) Concept of a Manufacturing system. International Journal of Production Research 17(2):123 –34 Pegden C (2005) Future directions in simulation modeling. In: Proceedings of the 37th Winter Simulation Conference, pp 1–35

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Pidd M (1992) Guidelines for the design of data-driven generic simulators for specific domains. Simulation 59(4):237–243 Randell L, Bolmsjö G (2001) Database driven factory simulation: A proof-ofconcept demonstrator. In: Peters B, Smith J, Medeiros D, Rohrer M (eds) Proceedings of the 33rd conference on Winter simulation, December 9-12, pp 977– 983 Robinson S (2004) Simulation: The practice of model development and use. John Wiley & Sons, Chichester Smith J (2003) Survey on the use of simulation for manufacturing system design and operation. Journal of Manufacturing Systems 22(2):157–171

Chapter 13

The Best of Both Worlds - Integrated Application of Analytic Methods and Simulation in Supply Chain Management Reinhold Schodl

This work attempts to discover how complex order fulfillment processes of a supply chain can be analyzed effectively and efficiently. In this context, complexity is determined by the number of process elements and the degree of interaction between them, as well as by the extent variability is influencing process performance. We show how the combination of analytic methods and simulation can be utilized to analyze complex supply chain processes and present a procedure that integrates queuing theory with discrete event simulation. In a case study, the approach is applied to a real-life supply chain to show the practical applicability.

13.1 Combination of Analytic Methods and Simulation Analytic models and simulation models are opposing ways to represent supply chain processes for purposes of analysis. “If the relationships that compose the model are simple enough, it may be possible to use mathematical methods (such as algebra, calculus, or probability theory) to obtain exact information on questions of interest; this is called an analytic solution” (Law and Kelton, 2000). Conversely, simulation models are quantitative models, which do not consist of an integrated system of precisely solvable equations. “Computer simulation refers to methods for studying a wide variety of models of real world systems by numerical evaluation using software designed to imitate the system’s operations or characteristics, often over time” (Kelton et al, 2002). The use of analytic models and simulation models in supply chain management harbors distinct merits and demerits (see Table 13.1). By combining analytic methods and computer simulation, one can potentially derive greater value than by applying one of these methods alone. This idea has been advocated since the early Reinhold Schodl Capgemini Consulting, Lassallestr. 9b, 1020 Wien, Austria, e-mail: : [email protected]

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Table 13.1 Analytic models compared to simulation models Strengths of Analytic Models

Strengths of Simulation Models

No limitation to descriptive models, as analytic models can be prescriptive (i.e., optimization models) as well

Ability of representing systems with comprehensive stochastic cause-effect-relationships

High significance of results (conversely, conclusions derived from stochastic simulation carry risk, because analysis is based on a limited sample size of output values generated by repeated simulation runs)

Possibility to determine not only mean values, but also distributions of output variables by approximation

Lower time and effort to adapt an existing analytic model compared to building a new simulation model (as simulation models are generally built case-specific)

High acceptance among practitioners, as often better understandable and more transparent than analytic models (especially when animations are being added to simulation models)

days of computer simulation. Nolan and Sovereign integrate analytic methods with simulation in an early work in the area of logistics (Nolan and Sovereign, 1972). Later research utilizes the joint application of the methods in the field of supply chain management (for examples, see Ko et al, 2006; Gnoni et al, 2003; Merkuryev et al, 2003; Lee and Kim, 2002). Depending on the degree of integration, one can distinguish two different forms, i.e., hybrid modeling and hybrid models. “Hybrid modeling consists of building independent analytic and simulation models of the total system, developing their solution procedures, and using their solution procedures together for problem solving” (Sargent, 1994). An example is the evaluation of alternatives based on economic viability and operative feasibility by applying an analytic and a simulation model respectively. A further application is the verification of an analytic model via an independent simulation model (Jammernegg and Reiner, 2001). “A hybrid simulation/analytic model is a mathematical model which combines identifiable simulation and analytic models” (Shanthikumar and Sargent, 1983). Hybrid models are characterized by a higher degree of integration, as analytic methods and simulation are incorporated into a single model. Hybrid models can be classified according to the type of dynamic and hierarchical integration (see Table 13.2). Following the classification with regard to dynamic integration, this work presents a Type I model. Concerning the hierarchical integration, the presented model is a special case of Type IV, as the simulation model requires the analytic model’s output, but both models are hierarchically equivalent and represent the whole system.

13 The Best of Both Worlds

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Table 13.2 Classification of hybrid models Dynamic Integration

Hierarchical Integration

Hybrid Model Type I: “A model whose behavior over time is obtained by alternating between using independent simulation and analytic models. The simulation (analytic) part of the model is carried out without intermediate use of the analytic (simulation) part” (Shanthikumar and Sargent, 1983)

Hybrid Model Type III: “A model in which a simulation model is used in a subordinate way for an analytic model of the total system” (Shanthikumar and Sargent, 1983)

Hybrid Model Type II: “A model in which a simulation model and an analytic model operate in parallel over time with interactions through their solution procedure” (Shanthikumar and Sargent, 1983)

Hybrid Model Type IV: “A model in which a simulation model is used as an overall model of the total system, and it requires values from the solution procedure of an analytic model representing a portion of the system for some or all of its input parameters” (Shanthikumar and Sargent, 1983)

13.2 Hybrid Models for Complex Supply Chains The analysis and improvement of complex supply chain processes is a unique challenge. Given the fact there is no universally accepted definition of the complexity of supply chain processes, we define the following building factors for complexity: number of process ele-ments (e.g., activities, buffers, information, resources) and degree of interaction between them, random variability (e.g., machine failures), and predictable variability (e.g., multiple product variants). The following two approaches show that hybrid models are particularly suitable for the analysis of complex supply chain processes. • The entire system is assessed by using analytic methods (e.g., queuing theory). Subsequently, the results of the assessment are used to construct a model of a sub-system, which then helps to conduct a more detailed analysis by means of simulation. This type of approach is used, for instance, to analyze a complex supply chain in the semi-conductor industry (Jain et al, 1999). • An analytic model is employed to assess a relatively large number of alternatives with relatively minimal effort. Promising alternatives are analyzed via simulation in more detail. For instance, such approach is employed to solve complex transportation problems (Granger et al, 2001). We now present a procedure to analyze complex supply chains with a balance between validity and effort. The procedure is different from the discussed approaches in the following ways. First, narrowing of the system’s scope by an analysis on an aggregated level is avoided, to incorporate the dynamic behavior of the overall system. Second, no preselecting of alternatives by an analysis on an aggregated level occurs, which prevents an unwanted rejection of promising process designs. The procedure consists of the following steps:

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1. In the first step, the real system’s supply chain processes are modeled as an analytic model and analyzed according to queuing theory. The queuing model delivers values of performance indicators (e.g., waiting times) which are inputs for the complexity reduction in Step 2, as well as for the simulation model in Step 3. 2. This step aims to reduce complexity by identifying non-critical process steps that can be modeled in a simplified manner in Step 3. If variability is not being reduced, it has to be buffered by inventory, capacity, or times in order to maintain process performance. Inventory levels, capacity utilization, and waiting times represent the degree of buffering, and therefore act as indicators of how critical a process step is. These indicators can be obtained from the queuing model. Further indicators can be derived from the real system. An example is a process step’s relative position in the queuing network as, generally, variability at the beginning of the process has greater impact than at the end. 3. In this last step, the supply chain processes are modeled as discrete event simulation model. Process steps that are defined in Step 2 as non-critical are modeled in a simplified manner. Simplification can be achieved by modeling process steps without capacity restrictions. Waiting times caused by capacity limitations are then modeled in the simulation model as constants according to the values derived from the queuing model. Finally, the simulation model is applied to analyze alternative process designs.

13.3 Application in Supply Chain Management To demonstrate the practical applicability, we applied the described procedure to a supply chain in the electronic industry, with focus on a first-tier supplier producing printed circuit boards. In a period of six months, 407 different products consisting of 817 different components are produced by 325 machines. The value-adding processes are heavily influenced by a highly variable demand as a result of short-term market trends, as well as by frequent disruptions of production due to the application of complex technologies. The overall aim of the case study is to improve service levels while taking cost constraints into account. In particular, two design alternatives are considered and compared with the initial situation: first, capacity enlargement for the main bottleneck work centers and second, implementation of the concept Make-to-Forecast (Raturi et al, 1990) based on improved short-term forecasts by using data available from Vendor Managed Inventories. The core of the case study consists of three steps, as described below.

13.3.1 Step 1: Analysis Based on Analytic Methods The supply chain processes are modeled as a network of queues to be analyzed according to queuing theory. The software MPX (Network Dynamics, Inc.) is applied,


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which “... is based on an open network model with multiple classes of customers. It is solved using a node decomposition approach. [Each] ... node is analyzed as a GI/G/m queue, with an estimate for the mean waiting time based on the first two moments of the arrival and service distributions. Next, the MPX solution takes into account the interconnection of the nodes ... as well as the impact of failures on the service time and departure distributions” (MPX, 2003). The analytic model’s inputs include: • Demand data (primary demand in defined period, variability of customer order inter-arrival time), • Bill of material data, • Routing data (sequence of production steps, average setup time, variability of setup time, average process time, variability of process time, work center assignment), • Resource data (parallel machines in work centers, scheduled availability, mean time to failure, mean time to repair), and • Production lot sizes. The model is validated by comparing the mean production lead time with that of the real system, which differs by less than 5%. It is then applied to find values for each work center’s capacity utilization and average value-adding times for setting-up and processing, as well as average waiting times due to capacity restrictions. This output is required for the reduction of complexity in Step 2 and for the simulation model in Step 3.

13.3.2 Step 2: Reduction of Complexity If certain resources, such as work centers, are not modeled in the simulation model, the effort for building and running the model can be reduced. This is acceptable only if simplified modeling is limited to resources aligned to non-critical process steps. Process steps are classified as critical and non-critical based on multiple criteria, as follows: • The capability of a process step to deal with variability is an important factor in evaluating how critical a process step is. Generally, if variability cannot be reduced, it has to be buffered by capacity, time, and inventory. Fundamental indicators for the degree of buffering of variability are capacity utilization and lead time efficiency. Both measures are provided by the described queuing model. • Another factor is the relative contribution of a process step to the overall performance of the supply chain, which can be measured by a process step’s proportion of value-adding time and proportion of cost of goods sold. • Moreover, a process step’s relationship with other process steps is taken into account. The relative position of a process step within the network is a relevant indicator, as generally variability at the beginning of a process has greater impact than at its end. A further indicator is a process step’s assembling functionality,

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as asynchronous arrival from previous process steps, is an important cause for delays.

13.3.3 Step 3: Simulation-Based Analysis The processes of the supply chain under study are modeled as a simulation model to be analyzed in detail with multiple performance measures. After building the model, verification and validation is carried out and an experimental design is developed to finally run simulation experiments. Critical process steps are modeled detailed, i.e., resources that carry out the process steps are represented in the model, including details about scheduled availability and random breakdowns. Resources aligned to non-critical process steps are not being modeled. Because of this simplification, waiting times caused by capacity restrictions cannot be determined by the simulation model. Thus, for non-critical process steps, the waiting times calculated by the analytic model are utilized and represented as constants in the simulation model. This approach guarantees a balance between representing reality as detailed as necessary while also keeping the effort to build and run the model as low as possible. The case study’s discrete event simulation model is implemented with the software ARENA (Rockwell Automation), which is based on the simulation language SIMAN. The simulation model accounts for various risks of the supply chain, especially variable demand, forecast errors, stochastic setup times and machine breakdowns. The model’s input is comprised of: • Demand data (order time, order quantity, desired delivery date), • Forecast data (forecasted order time, forecasted order quantity, forecasted desired delivery date), • Bill of material data, • Routing data (sequence of production steps, assignment of work centers, setup time, processing time), • Resource data (parallel machines in work center, scheduled availability, mean time to failure, mean time to repair, constant waiting time for simplified modeled work centers), • Production data and rules (production lot size, rule for dispatching production orders, rule for prioritization of production orders), and • Cost data (material cost, time-depended machine cost, quantity-depended machine cost). The length of the warm-up-period of the non-terminating simulation is decided by visual analysis of the dynamic development of inventory. The number of replications is determined by statistical analysis of the order fulfillment lead time. The output of the simulation model comprises performance measures whose definitions are in line with the well-established Supply Chain Operations Reference Model (Supply Chain Council, 2009). The defined scenarios are compared with


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multiple performance measures, i.e., delivery performance, order fulfillment lead time, capacity utilization, cost of goods sold, and inventory days of supply. Table 13.3 Effect of complexity reduction Degree of Complexity Reduction.

Error of Order Fulfillment Lead Time.

0% 9% 29%

0.60% 1.00% 2.90%

The focus of this paper does not lie in the presentation of the scenario’s specific results, but on a demonstration of the practical applicability of the presented approach to deal with complex supply chains. Therefore, the validation of the simulation model under different degrees of complexity reduction is of particular interest. The degree of complexity reduction is expressed as the proportion of work centers modeled in a simplified manner. Table 13.3 shows how complexity reduction affects the model’s error of order-fulfillment lead time. Complexity reduction of 9% results in a generally acceptable error of the order fulfillment lead time of 1%; for a complexity reduction of 29%, the error is still under 3%. For further validation, statistical analysis of the order fulfillment lead times of the customer orders was carried out. A Smith-Satterthwaite test is utilized, as the system and model data are both normal and variances are dissimilar (Chung, 2004). For a level of significance of 0.05 and a degree of complexity reduction of zero and 9%, there is no statistically significant difference between the actual system and the simulation. For a level of significance of 0.01, this is also true for a complexity reduction of 29%.

13.4 Conclusion Analytic models and simulation models are characterized by specific strengths and weaknesses. In this paper, we demonstrated a procedure that combines an analytic queuing model with a discrete event simulation model to utilize the specific benefits of both methodological approaches. A balance between validity of the results and effort for the analysis of the supply chain processes was accomplished.

References Chung C (2004) Simulation modeling handbook: A practical approach. CRC Press, Boca Raton

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Gnoni M, Iavagnilio R, Mossa G, Mummolo G, Di Leva A (2003) Production planning of a multi-site manufacturing system by hybrid modelling: A case study from the automotive industry. International Journal of production economics 85(2):251–262 Granger J, Krishnamurthy A, Robinson S (2001) Stochastic modeling of airlift operations. In: Proceedings Winter Simulation Conference 2001, IEEE Computer Society Washington, DC, USA, vol 1, pp 432–440 Jain S, Lim C, Gan B, Low Y (1999) Criticality of Detailed Modeling in Semiconductor Supply Chain Simulation. In: Proceedings of the Winter Simulation Conference 1999, ACM New York, NY, USA, vol 1, pp 888–896 Jammernegg W, Reiner G (2001) Ableitung und Bewertung von Handlungsalternativen in einem Unternehmen der Elektroindustrie. In: Jammernegg W, Kischka PH (eds) Kundenorientierte Prozessverbesserungen, Konzepte und Fallstudien, Springer, Berlin, Berlin, pp 237–247 Kelton W, Sadowski R, Sturrock D (2002) Simulation with ARENA, 2nd edn. McGraw-Hill Science/Engineering/Math, Boston Ko H, Ko C, Kim T (2006) A hybrid optimization/simulation approach for a distribution network design of 3PLS. Computers & Industrial Engineering 50(4):440– 449 Law A, Kelton W (2000) Simulation modeling and analysis, 3rd edn. McGraw Hill, New York Lee Y, Kim S (2002) Production–distribution planning in supply chain considering capacity constraints. Computers & Industrial Engineering 43(1):169–190 Merkuryev Y, Petuhova J, Grabis J (2003) Analysis of dynamic properties of an inventory system with service-sensitive demand using simulation. In: Proceedings of the 15 th European Simulation Symposium-Simulation in Industry, Delft, The Netherlands, pp 509–514 MPX (2003) MPX WIN 4.3 - For use with Windows, User Manual. Network Dynamics Inc, Framingham Nolan R, Sovereign M (1972) A recursive optimization and simulation approach to analysis with an application to transportation systems. Management Science 18(12):676–690 Raturi A, Meredith J, McCutcheon D, Camm J (1990) Coping with the build-toforecast environment. Journal of Operations Management 9(2):230–249 Sargent R (1994) A historical view of hybrid simulation/analytic models. In: Proceedings of the Winter Simulation Conference, pp 383–386 Shanthikumar J, Sargent R (1983) A unifying view of hybrid simulation/analytic models and modeling. Operations Research 31(6):1030–1052 Supply Chain Council (2009) SCOR Model. URL http://www.supplychain.org/cs/root/s/scor model/scor model

Chapter 14

Rapid Modeling In A Lean Context Nico J. Vandaele and Inneke Van Nieuwenhuyse

Abstract Lean management is widespread but theoretical models that scientifically substantiate the lean practice are scarce. We show how queuing models of manufacturing systems and supply chains underpin the practice of Lean. Two quantitative performance models which relate the system parameters with the system performance in terms of lead time and throughput will be discussed, including an exogenous definition of Lean. We show that the ideal level (i.e., the Lean level) of the system buffers (safety capacity, work-in-process and safety time) are determined by the targeted system performance. Moreover, the lean concept is dynamic in nature: when either system characteristics or target performance change, the lean buffer levels change accordingly. The latter stresses the need for a comprehensive, analytical and consistent approach. This quantitative approach will be illustrated with lead time and throughput models.

14.1 Introduction In industrial practice, the concept of Lean operations management is the hype of the new millennium. It consists of a set of tools that assist in the identification and steady elimination of waste (muda), the improvement of quality, and production time and cost reduction. The concept of Lean operations is built upon decades of insights and experience from Just-In-Time (JIT) applications. Since the first articles and books Nico J. Vandaele Research Center for Operations Management, Department of Decision Sciences and Information Management, K.U. 3000 Leuven, Belgium, e-mail: [email protected] Inneke Van Nieuwenhuyse Research Center for Operations Management, Department of Decision Sciences and Information Management, K.U. 3000 Leuven, Belgium, e-mail: [email protected]

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appeared, a tremendous number of publications became available for the practitioner (e.g. Womack et al (1990), Womack and Jones (1997), Liker (2004)). Many big companies adopted company-wide leadership programs to get their company on the lean track. In academia, the Lean concept has received rather limited attention, based on the reproach that Lean did not offer much more on top of the traditional JIT body of knowledge, and hence should be qualified primarily as a philosophy without rigorous scientific foundations. This is only partly true. It is indeed true that the scala of lean management techniques is often rather descriptive, failing to offer analytical modeling and/or optimization tools that could guide managerial decision making. Cosnider for instance the heavily promoted tool Value Stream Mapping as presented in the best seller ‘Learning To See’ (Rother and Shook, 1999). Value Stream Mapping forces to map the logical structure of the processes and adds valuable quantitative data both on system parameters as on performance measures. However, Value Stream Mapping is incapable to give insight in the relationships between the data and performance measures as well as the links between various elements of the mapped processes. In this paper, we present two quantitative models to underpin the definition of lean in terms of the lead time and the throughput of a flow system. As will be shown, the quantification of Lean boils down to an adequate match between the system’s parameters and target system performance. A mismatch between the two can cause a system to be either obese, or anorectic.

14.2 The Quantification Of Lean In order to develop a quantitative approach to the Lean concept, we will rely on some basic stochastic models for flow systems. Flow systems are systems where a set of resources is intended to perform operations on flows (see Vandaele and Lambrecht, 2003). Some illustrative examples are listed in table 14.1. Table 14.1 Some flow system examples Flow System

Typical Resources

Typical Flows

Production line Production Plant Hospital Airport Traffic Roads Laboratory Equipment Computer network Mobile phone network Insurance company

Machines, workers Machines, internal transport Hospitals beds, physicians, nurses Counters, desks traffic lights laboratory assistants Servers data lines Antenna’s, transmitters, buffers Inspectors, account managers

Products Products Patients Passengers Cars, trucks Samples Data, messages Calls Files

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These examples show the rich variety of flow systems. All these systems share some common physical characteristics: on their routing through the system, flows visit resources in order to be processed, and hence consume (part of the) capacity of the resources. This competition for capacity causes congestion: flows may need to queue up in front of the resources. This congestion in turn inflates the lead time of a flow entity through the system. These basic mechanics of a flow system imply that every decision related to the flow has consequences for the resource consumption over time. For instance, once lead time off-setting for manufacturing components in an assembly setting is performed, resources (i.e., capacity) need to be committed in order to be able to perform the required processes for the components. Vice versa, all resource-related decisions have an impact on the flow: scheduled maintenance for instance will temporarily impede flow, while sequencing decisions cause certain flows to proceed while other flows need to wait. Consequently, flow systems contain three fundamental decision dimensions: flows, resources and time. If a flow system is to be managed in an effective and efficient way, the management decisions must consider the flow, resource and time aspects simultaneously, symbolized by the intersection visualized in Fig.14.2.

Fig. 14.1 The basic dimensions and buffers of a flow system

In what follows, we assume the flow system to be stochastic: i.e. both the flows and the resources are subject to variability. In real-life systems, causes of system variability are omnipresent, like quality problems, resource failures, stochastic routings, randomness, etc. (see for instance Hopp and Spearman, 2008). It is known that the presence of variability influences system performance in a negative way (Vandaele and Lambrecht, 2002). Important system performance measures are resource utilization, flow time, inventory, throughput and various forms of service level. Some of these (e.g. flow time and inventory) are flow oriented, while others (such as utilization and throughput) are resource oriented. In order to maintain an acceptable performance in a stochastic environment, a flow system has to operate with buffers (Vandaele and De Boeck, 2003). Conform the three basic system dimensions mentioned above, three types of buffers may be used: inventory buffers (e.g. safety stocks, work-in-process,), capacity buffers (spare capacity, temporary labor,) and time buffers (safety time, synchronization buffers,...). Any particular combination of the three buffers leads eventually to a

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specific performance level. These buffers can be interchanged in order to reach a desired performance level. For instance, short lead times combined with the absence of work-in-process -mandatory in e.g. Just-In-Time systems- can only be guaranteed with lots of excess capacity. The amount of excess capacity (capacity buffer) can be reduced if variability and/or randomness are eliminated (see Hopp and Spearman, 2008). Tight capacity typically leads to high utilization at cost of long lead times and high work-in-process. Consequently, there may be several combinations of fundamental buffers leading to the same performance. These can be considered as some kind of technically equivalent buffer combinations. A monetary evaluation in terms of costs and revenues, can lead to the best economic choice between the technically equivalent options. The nature of the system largely determines which type of buffer is feasible (theoretically, or in practice). For instance, service systems do not have the possibility to employ an inventory buffer. Legal advice or consulting services are typical examples. Likewise, large time buffers in emergency systems (fire brigades, medical rescue teams) are unacceptable. As a consequence, these systems are known to operate with huge amounts of safety capacity. In this view, a system is defined as “Lean” when the buffers present in the system are restricted to the minimum level necessary in order to support the target performance (Hopp and Spearman, 2008). This is referred to as the Lean level. Consequently, all buffering in excess of that necessary minimum can be considered as obese, in the meaning that there is too much buffering for the desired performance. This state of obesity can manifest itself into too much inventory, too much safety time or overcapacity. An obese system could reach its target performance with either smaller buffers, or a better allocation of buffers. If these excess buffers are systematically reduced while keeping up with the desired system performance, the systems gets leaner. However, excessive reduction of buffers will cause system performance to erode: the target performance will eventually become unachievable. In these situations, we characterize the system as anorectic. Note that the above definition of Lean is not static, as it depends both on the system characteristics and the targeted performance. Consequently, the stronger the stress on the system’s performance measures, the more buffers (minimally) will be necessary: hence, the Lean level will change. The specific Lean level of a system may also differ across different systems. For example, the right amount of safety capacity for a car assembly plant compared to a truck manufacturer is different if they both want to be considered lean for similar performance objectives (e.g. a customer order delivery time of three months). Further, if the performance objectives vary through time (for instance with increased competition), the Lean level will change to reflect the new conditions. Note also that the system’s characteristics vary over time (e.g. the inherent variability of the system may decrease as a consequence of system improvements, product mix changes, etc.). This also impacts the Lean level. Following these arguments, the definition of Lean is dynamic in nature. We will now illustrate these concepts with two basic stochastic models, an M/M/1 queuing model and a model of a production line with limited work-in-process allowance.

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14.2.1 Lead Time: Safety Time Versus Safety Capacity In this section we consider a system consisting of only one single server, processing a single product type. The system’s queueing behavior can be modeled as an M/M/1 system (see e.g. Anupindi et al, 2006), with an arrival rate μ and a processing rate μ . The desired customer service levvel is defined by S (0<S

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