Collaborative Planning in Supply Chains: A Negotiation-Based Approach

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Collaborative Planning in Supply Chains Second Edition

Gregor Dudek

Collaborative Planning in Supply Chains A Negotiation-Based Approach Second Edition

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Dr. Gregor Dudek Neuweg 15 55130 Mainz Germany [email protected]

ISBN 978-3-540-92175-2 e-ISBN 978-3-540-92176-9 DOI 10.1007/978-3-540-92176-9 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2008943005 c Springer-Verlag Berlin Heidelberg 2004, 2009 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, 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 protective laws and regulations and therefore free for general use. Originally published in Lecture Notes in Economics and Mathematical Systems, Vol. 533. Cover design: WMXDesign, Heidelberg Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

Foreword to the Second Edition There are only a few cases where a PhD thesis has been published in a second edition. And not only the PhD thesis by Gregor Dudek has received great attention and thus required a second edition, but also his two papers published in the European J. of Operational Research in 2005 and in the International J. of Production Research in 2007 have inspired a great number of researchers to consider collaborative planning as a rewarding and practice-oriented research area. Although the hype of Advanced Planning Systems (APS) has somewhat gone, the need to coordinate plans within a supply chain consisting of separate legal entities each with its own planning domain still exists. I very much welcome that Gregor Dudek has made great efforts to review recent publications in this area and to include these in this second edition of his PhD thesis. Still, there is much room for future research, e.g. with respect to incentives for self-interested parties to participate in negotiations and to be truth-telling. Thus, it is hoped that this second edition will inspire even more young researchers to take up the challenge and to be as successful as Gregor Dudek. Hamburg, October 2008

Hartmut Stadtler

Foreword to the First Edition In light of the vast number of publications on Supply Chain Management (SCM) it is not easy to extract those which will have a great impact both on theory and practice. The dissertation of Gregor Dudek certainly is one such valuable source because it tackles inter-organizational collaboration in a novel and effective manner. SCM is concerned with the coordination of material, information and financial flows within and across often legally separated organizational units. It has gained great attention both in industry and research as an important area for improving competitiveness. A Supply Chain (SC) can be regarded as a hybrid between a market relationship and a hierarchical organization and as such requires specific tools to support the efficient planning and execution of the order fulfillment process. Software vendors have developed so called Advanced Planning Systems (APS) to overcome deficiencies of traditional Enterprise Resource Planning systems and to better support the planning functions needed in SCM. However, APS are based on the principles of hierarchical planning which are well-suited for intraorganizational SCs but fall short when non-hierarchical collaboration between partners (companies) is needed. This is particularly true when a buyer and a supplier have to align their medium term order and supply plans. This is the starting point of the dissertation of Gregor Dudek. He devises a negotiation-based collaborative planning scheme that coordinates master plans of two individual SC partners each with his own planning domain (APS). Extensions to more general two tier SC structures are provided too. The basic idea of the negotiation scheme is that order proposals (generated by buyers) and supply proposals (generated by suppliers) are exchanged between SC partners in an iterative manner. The proposal received from a SC partner is analyzed for its consequences on local (master) planning, and a counter-proposal is generated by introducing partial modifications. Resulting is a negotiation-based process which subsequently improves SC wide costs without centralized decision making and with limited exchange of information between the partners. Specifically, only the respective order / supply proposals and associated cost effects are exchanged between SC partners. As a generic model for master planning – although not limited to it - a multilevel, capacitated, lot-sizing model (MLCLSP) is assumed. The MLCLSP is then enlarged by additional variables and constraints to mimic the specific tasks of the model in the negotiation process. Here, the generation of a compromise proposal – along the lines of Goal Programming – has to be mentioned as one of the novel features of Dudek´s research. Several valuable extensions to the basic negotiation scheme are discussed, like rolling schedules or possible compensation schemes in light of psychological experiments, contract theory, game theory, controlling and common sense. Extensive computational tests show that the proposed negotiation scheme results in less SC wide costs than achievable by pure Upstream Planning and even

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Foreword to the First Edition

comes near to the minimum cost solutions of central planning after only a few (i.e. about five) iterations. In summary Gregor Dudek has developed a negotiation scheme for coordinating master plans between SC partners which • avoids the exchange of critical information like cost and capacities, i.e. only uses (uncritical) order and supply proposals by partners, • comes near to the minimum cost of central planning, • and requires only a few negotiation rounds (iterations). Since the proposed negotiation scheme can already by applied by SC partners today by making use of APS and existing Collaborative Planning modules research results of this dissertation will have a great impact on the theory and practice of SCM. The extraordinary quality of his contribution has also been acknowledged by the jury of the Management Science Strategic Innovation Prize (MSSIP) by ranking a related paper as the second best among all submitted publications in the 2003 contest. Darmstadt, August 2003

Hartmut Stadtler

Preface to the Second Edtion Five years have passed since the original version of my dissertation was submitted to the Darmstadt University of Technology and published in the “Lecture Notes in Economics and Mathematical Systems” at Springer. Over these years, the practices of Supply Chain Management and the use of Advanced Planning Systems became more white-spread and applied in many companies. Personnally, I have witnessed this development, and supported it to a little extent, with my own work in management consulting for four years, and since a year at an industrial goods company. Despite the increasing use of Advanced Planning, the interface to independent supply chain partners (suppliers and customers) still remains a major challenge in the practice of supply chain integration. Many companies exchange an increasing amount of supply chain information with their business partners, but still are far from applying a structured Collaborative Planning process. In the supply chain I deal with, we e.g. share forecasts with key customers and suppliers on a weekly or monthly basis, and at times “negotiate” changes to a partners’s forecast. However, this happens without much decision support or a formalized process. Thus, Collaborative Planning remains a topic, which needs to be further explored, in practice as well as in academics. I am therefore proud and very thankful for the chance to publish a second, revised edition of my original work, which tries to incorporate some of the developments of the last years. But what exactly does the new edition bring about to you, the reader? In summary, the new edition is hoped to be a source on Collaborative Planning, which is on the one hand up-to-date in terms of literature and references, and on the other hand more readable and easier to understand. There are three major types of updates to the original text: • Literature references are updated and references to new, interesting publications are added. This applies especially to chapters 2 (Overview of Supply Chain Management and Collaborative Planning) and 3 (Modeling Framework and Relevant Literature). • Secondly, the complete text is reworked in order to make it more digestable. To achieve this, some parts of the text were restructured (e.g. section 3.3) and others shortened (e.g. various sections of chapter 4). Across the whole text, the language was simplified where possible and unnecessarily long explanations shortened. • Finally, a list of “key points” was added at the beginning of each chapter, which shows the key messages that are conveyed in the subsequent sections. Also, selected references are given at the end of each chapter for interested readers. This revision could not have been achieved without the support of a number of helpful hands! My thanks go to Herbert Meyr, in the meantime professor for Production and Supply Chain Management at the Darmstadt University of Technology, and Martin Albrecht from the University of Hamburg for providing access to

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Preface to the Second Edition

literature and hints on interesting publications; Professor Hartmut Stadtler for discussing the amount of updates and revisions; and finally Katharina Wetzel-Vandai from Springer, who made the second edition possible, and gave all the necessary technical support to achieve this undergoing. Mainz, October 2008

Gregor Dudek

Preface to the First Edtion The following dissertation is the outcome of a three-year research effort at the department of Production and Supply Chain Management of the Darmstadt University of Technology. When this work started in mid of 2000, the term “Collaborative Planning” was about to gain popularity, especially in practitioner-oriented publications on Supply Chain Management. Yet, in searching these publications for answers to questions of how a Collaborative Planning process should actually look like, or which goals and objectives it should serve, one quickly found that most contributions only scratched at the surface of Collaborative Planning. Most frequently, discussions focused on the technological means available for the exchange of information between independent Supply Chain partners, such as Email, Web-interfaces, or the XML technology. While the technological perspective is an important aspect, it is by itself not sufficient to realize a Collaborative Planning process. Therefore, the goal of this dissertation is to provide a process model which is concerned with the decision making and negotiation aspects of Collaborative Planning. Taking necessary technological means as a given, it sketches a detailed picture of a Collaborative Planning process at the medium-term level of Master Planning, and indicates how financial and contractual aspects are affected by the negotiations of supply quantities between buyers and suppliers. This work could not have been realized without the advice and guidance of numerous supporters. First and foremost, I like to thank my adviser Hartmut Stadtler. He not only proposed the topic of the dissertation as a potential gap in existing research on Supply Chain Management, but also gave crucial advice throughout all stages of the work. I am also very thankful to Ton de Kok from the Eindhoven University of Technology for his willingness to serve as the co-adviser and second referee of the dissertation. His general interest in the work along with numerous hints and comments helped to improve the quality of the dissertation substantially. Equally important for the progress of the project were the steady debates and discussions with colleagues and co-workers. I especially like to thank Jens Rohde and Christopher Sürie from the Darmstadt University of Technology as well as Norbert Wenig from the SAP AG. Finally, I am indebted to my family and friends for the support and encouragement on the one hand, but also for their constant reminds that there is a live beyond purely scientific matters. This applies in the first place to my girl friend Natalie Kappesser. Although actually practicing pediatrics, she not only accepted to become a Supply Chain expert in her own right, but also managed unambiguously to keep my feet on the ground. Mainz, August 2003

Gregor Dudek

Table of Contents

1 Introduction......................................................................................................1 2 Supply Chain Management and Collaborative Planning.............................5 2.1 The Concept of Supply Chains.....................................................................5 2.2 Overview of Supply Chain Management .....................................................7 2.3 Operations Planning in Supply Chains.......................................................12 2.3.1 Successive and segregated planning...................................................13 2.3.2 Hierarchical planning .........................................................................15 2.3.3 Collaborative planning .......................................................................19 3 Modeling Framework and Relevant Literature ..........................................25 3.1 Modeling ...................................................................................................25 3.1.1 Decision situation and modeling assumptions....................................25 3.1.2 Intra-domain planning model .............................................................30 3.1.3 Modeling links to adjacent planning domains ....................................35 3.2 Benefits of Information Sharing and Collaboration ...................................37 3.3 Coordination of Planning Processes Along the Supply Chain ...................42 3.3.1 Coordination by contracts ..................................................................42 3.3.2 Coordination mechanisms for mathematical programming models ...46 4 Negotiation-Based Collaborative Planning between Two Partners...........57 4.1 Assumptions and Overview .......................................................................57 4.2 Iterative Planning Steps..............................................................................61 4.2.1 Evaluating the partner proposal..........................................................62 4.2.2 Determining the preferred outcome....................................................63 4.2.3 Generating a compromise proposal ....................................................69 4.2.4 Generating additional compromise proposals ....................................83 4.3 Collaborative Planning Process in Total ....................................................91 4.3.1 Data exchange requirements ..............................................................91 4.3.2 Total process flow ..............................................................................94 4.3.3 Stopping criteria .................................................................................97 4.4 Summary and Comments .........................................................................101 5 Extensions to the Basic Collaborative Planning Scheme..........................103 5.1 Extended Supply Chain Structures...........................................................103 5.1.1 General two-tier supply chains.........................................................103 5.1.2 Multi-tier supply chains....................................................................112 5.2 Planning on a Rolling Basis .....................................................................115 5.2.1 Conceptual overview........................................................................118 5.2.2 Extensions to process flow and planning models .............................120

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Table of Contents

5.3 Limited Exchange of Cost Information.................................................... 125 5.3.1 Limited exchange between two planning partners ........................... 125 5.3.2 Limited exchange between multiple planning partners.................... 127 5.3.3 Limited exchange in planning on a rolling basis.............................. 129 6 Implications on Supply Contracts and Partner Incentives ...................... 131 6.1 Contractual Consequences ....................................................................... 131 6.1.1 Compensation and savings sharing .................................................. 132 6.1.2 Adaptation of supply contracts......................................................... 140 6.2 Potentials of Opportunistic Behavior and Counteractions ....................... 147 6.2.1 Game-theoretic analysis ................................................................... 147 6.2.2 Means preventing opportunistic behavior ........................................ 158 7 Computational Evaluation.......................................................................... 165 7.1 Implementation of the Collaborative Planning Scheme........................... 165 7.2 Generation of Test Instances.................................................................... 168 7.3 Tests with a Single Buyer and Supplier ................................................... 173 7.3.1 Test classes and test program ........................................................... 173 7.3.2 Overview of test results.................................................................... 178 7.3.3 Results by cost structure, utilization profile, and iteration ............... 186 7.3.4 Results with limited exchange of cost information .......................... 190 7.4 Tests with One Supplier and Several Buyers ........................................... 193 7.4.1 Test classes and test program ........................................................... 193 7.4.2 Overview of test results.................................................................... 196 7.5 Tests with Rolling Schedules ................................................................... 201 7.5.1 Test classes and test program ........................................................... 201 7.5.2 Test results with deterministic demand ............................................ 203 7.5.3 Test results with uncertain demand .................................................. 207 8 Summary and Conclusions ......................................................................... 215 References .......................................................................................................... 219 List of Figures .................................................................................................... 229 List of Tables ..................................................................................................... 231 List of Symbols .................................................................................................. 233

1

Introduction

This book deals with collaborative planning between supply chain partners, that is independent companies or business units of large corporations, which develop close relationships in the course of engaging in Supply Chain Management. Supply Chain Management is widely acknowledged as a major avenue to increase competitiveness and boost performance of businesses in today’s increasingly challenging business environment. It grounds on the idea to link and streamline business processes along the supply chain, i.e. the network of organizations involved in creating final customer products and services. This particularly applies to the core operational activities such as production, storage, and distribution processes, as these directly contribute to products and services offered in the marketplace and incur significant portions of costs and capital needs. The coordination of operational processes across the supply chain thus bears the potential to enhance customer service and reduce operating costs. One approach to achieve coordination of operational processes is by centralized planning. The idea here is to synchronize operations by installing a central decision making unit which generates plans for all processes along the supply chain. Proponents of this solution usually suggest to implement hierarchical planning such that centralized coordination happens on a medium-term level, whereas it is left to the owners of the distinct operational processes to implement the results on the level of short-term planning and control. This approach appeals by the ease with which coordination is achieved and fits to the way in which decisions are made in hierarchical organizations. In fact, it is realized in Advanced Planning Systems (APS) offered by software vendors such as i2 and SAP. However, the downside of this solution is that the central coordinator needs access to all relevant information and the power to impose planning results on all organizational units. This requirement hampers its applicability to planning in decentralized firms and supply chains embracing independent business partners. Empirical evidence implies that, despite the benefits of supply chain integration, firms are reluctant to disclose sensitive information to supply chain partners. Moreover, the implementation of centralized planning in supply chains with independent partners can fail, simply because individual partners are involved in several supply chains; for example component suppliers in the automotive or electronics industry usually serve several large customers. Nonetheless, there is little doubt that significant efficiency potentials exist at the interfaces between independent supply chain partners, waiting to be unlocked by supply chain integration that goes beyond company borders. For example, Lowe / Markham (2001) report that winners of the 2001 “Global Excellence in Operations” award leverage supplier relationships and realize joint savings by synchronized delivery, inventory management, and planning and scheduling.1

1

C.f. Lowe / Markham (2001), pp. 52.

G. Dudek, Collaborative Planning in Supply Chains, 2nd edn., DOI 10.1007/978-3-540-92176-9_1, © Springer-Verlag Berlin Heidelberg 2009

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1. Introduction

Similarly, a study of consumer goods manufacturers conducted by Stank et al. (2001) reveals that industry leaders increasingly pursue “external integration” with customers and suppliers.2 Among the top means to achieve external integration the authors cite “cooperative planning”. Based on such findings, the question arises of how to realize cooperative planning between independent supply chain partners. This book contributes to this question by laying out a non-hierarchical, negotiation-based approach which can be applied to coordinate operational planning tasks of independent parties linked by supply relationships. It rests on the assumption that mathematical programming models are used by the individual partners to plan their respective operations. It introduces a coordination mechanism which ensures that consistent plans covering the entire supply chain are obtained with • the exchange of uncritical and as few as possible information, • as little computational and coordinating effort as possible, • demonstrably good solutions close to the “global optimum”. In a nutshell, the idea is to pass order proposals (generated by buyers) and supply proposals (generated by suppliers) between the parties in an iterative manner. A proposal received from a supply chain partner is analyzed for its consequences on local planning, and a counter-proposal is generated by introducing partial modifications. Resulting is a negotiation-like process which subsequently improves supply chain wide costs without centralized decision making and with limited exchange of information between the partners. Specifically, only the respective order / supply proposals and associated cost effects are exchanged between the partners. The text is structured as follows. In chapter two we introduce some basic definitions of supply chains and Supply Chain Management, and describe the distinct approaches to operations planning in supply chains in greater detail, namely centralized, hierarchical planning on the one hand and collaborative planning on the other. In chapter three we describe the mathematical modeling framework and review relevant literature. The focus first lies on mathematical programming models which can be used by the supply chain partners for planning of their internal operations. Subsequently, we report on findings from literature on the benefits of collaboration between supply chain partners and coordination of planning activities along the supply chain. Chapter four contains the core concepts developed here. It deals with the negotiation-based approach to collaborative planning between two supply chain partners, a single buyer and supplier. For laying out the scheme, the various, iterative steps carried out by each partner are described in detail, including modifications to the underlying mathematical programming models. Also, the entire process flow and control associated with the collaborative planning process is presented.

2

C.f. Stank et al. (2001), pp. 62.

1. Introduction

3

In chapter five, extensions are introduced to the basic collaborative planning scheme for two supply chain partners as developed in chapter four. First, we show how the concept can be modified in order to coordinate planning in more complex supply chain settings, namely in general two-tier supply chains comprising an arbitrary number of buyers and suppliers and in multi-tier supply chains. These extensions allow to apply the collaborative planning scheme not only to isolated buyer-supplier pairs, but to more general supply chain structures. Secondly, we elaborate on how the collaborative planning scheme can be modified for use in planning with rolling schedules. This, too, is an important enhancement of its basic form, as in practical applications planning is usually repeated periodically. Finally, modifications are introduced which allow to further restrict the amount of cost information exchanged between the supply chain partners. Chapter six deals with financial implications resulting from the collaborative planning scheme. In particular, the question of compensation and savings sharing is discussed and it is demonstrated how supply contracts can be modified in order to facilitate that the partners implement the results of collaborative planning. Also, incentives of opportunistic, i.e. non-cooperative, behavior by individual partners are analyzed. Finally, in chapter seven we report computational results obtained with the collaborative planning scheme and two other, benchmark, planning concepts. The tests show that the scheme yields favorable results in the vast majority of example problems. Major findings and conclusions of this work are summarized in chapter eight.

2 Supply Chain Management and Collaborative Planning Content This first chapter intends to give an overview of Supply Chain Management (SCM) and an introduction to Collaborative Planning. In particular, it shall be clarified how Collaborative Planning relates to SCM and why it can be considered an important component of implementing SCM. The concept and understanding of supply chains is introduced in section 2.1, followed by a brief overview of SCM in section 2.2. The remainder of the chapter is dedicated to operations planning in supply chains. The traditional concept of successive and segregated planning is shortly outlined, the focus is however set on two alternate approaches to coordinating operations along the supply chain: hierarchical planning one the one hand and collaborative planning as the theme of this work on the other. Key points • Supply Chain Management (SCM) can be regarded as cross-functional, intercompany business process management which tries to integrate and coordinate all the activities required to fulfill ultimate customer demand • Planning of operations (i.e. production, inventories, logistics activities) across the supply chain is a major component of SCM • Whereas operations planning traditionally happens in a segregated and successive way, a hierarchical approach is proposed within SCM. Here, centralized planning tasks (especially the medium-term master planning) coordinate and synchronize operations across the entire supply chain • Centralized planning in practice is however limited to parts of the overall supply chain (e.g. individual companies). Therefore, the idea of Collaborative Planning is to connect and coordinate planning tasks pertaining to indivudal SC members without the installation of a centralized, all-embracing decision making unit

2.1

The Concept of Supply Chains

Based on the often cited definition by Christopher (2005) a supply chain (SC) is defined as


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2. Supply Chain Management and Collaborative Planning

“the network of organizations that are involved, through upstream and downstream linkages, in the different processes and activities that produce value in the form of products and services in the eyes of the ultimate consumer”.3 The recognition of supply chains makes apparent that no single company or business unit fully controls manufacturing and distribution of its products. Instead, it also depends on the contribution of others and, just as important, the interactions between the various parties involved in the total process. Although the concept of SCs is well established and often referred to in the literature on marketing, logistics, operations management and other disciplines,4 its application to real-world businesses is not straight forward. First, it should be noted that the SC looks different from each party’s subjective perspective. For example, the SC of a manufacturer with several suppliers is not equivalent to the SC of one of the suppliers. This is because the supplier likely serves other customers, too, but has no direct business relations with the remaining suppliers. This is visualized in Fig. 1. Part a) represents the manufacturer’s SC and part b) the supplier’s one. The framed sections are common to both SCs. Second, trying to map a company’s SC raises at least two questions, namely: how many tiers of suppliers and customers should be regarded and at which level of detail. Principally, the SC might start at the stage of raw materials such as agricultural or mining products and go through to retail outlets of consumable products. However, with such as broad understanding one obtains highly complex, unmanageable networks. To better focus on activities that are of real relevance, Lambert et al. (1998) propose to differentiate between primary and supportive SC members.5 In analogy to Porter’s (1985) value chain model,6 primary members directly add value to the final products through their operations or services (e.g. component suppliers, logistical service providers), while supportive members provide resources that are consumed (e.g. equipment suppliers). a)

b)

S

S M

M

Fig. 1. Supply chains of a manufacturer and one of his suppliers

3 4 5 6

Christopher (2005), p. 17. See Croom et al. (2000) for an overview of subject areas dealing with SCs. C.f. Lambert et al. (1998), p. 5. See Porter (1985), pp. 36.

2.2. Overview of Supply Chain Management

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If only primary members are considered, the SC’s point of origin falls to where there are no direct suppliers and the point of consumption is where the product is no direct input but a consumed resource (e.g. an industrial machinery).7 Since the resulting network can still be large, a further limitation might be useful. Some authors therefore propose to consider only two tiers in the up- and downstream direction (the suppliers’ suppliers and the customers’ customers).8 Alternatively, one might try to evaluate which business partners are critical for and/or generally under the influence of the company of interest, and only consider these players in the SC. The appropriate level of detail to sketch a SC depends on the business context and managerial level. For example, when dealing with strategic relationships to business partners, the company itself and each supplier and customer might represent a single node of the network as depicted in Fig. 1. However, when logistical material flows are planned for, the various facilities of the company and its business partners usually each form a network node. Finally, it should be noted that SCs are sometimes regarded as a type of network organization, considered having characteristics that fall between verticallyintegrated systems and pure arms length market relationships.9 This view is not generally taken here. While the SC or a part of it might very well be managed like a network organization once Supply Chain Management techniques are applied, this is not per se the case. In fact, many of the deficiencies observed in SCs result from purely market-oriented interactions between their members.10

2.2

Overview of Supply Chain Management

The term Supply Chain Management was initially proposed to link logistics issues with strategic management.11 Early publications stress the growing importance of well-designed logistics processes in increasingly challenging business environments of the 1980’s. They propose intra-company integration of the purchasing, material handling, manufacturing and distribution functions and a reduction of inventory buffers.12 A similar understanding is expressed in many contemporary textbooks where SCM is often regarded as a synonymous term for integrated logistics management.13 However, a major difference concerns the scope attributed nowadays to SCM. Whereas initially an intra-firm perspective was predominant, 7 8 9 10 11 12 13

C.f. Lambert et al. (1998), p. 6. C.f. Stadtler (2005), p. 9. C.f. Cooper / Ellram (1993), pp. 13, Stadtler (2005), p. 15. For example the well-known bullwhip effect (see e.g. Lee et al. (1997), pp. 93). See e.g. Oliver / Webber (1992), p. 63, Houlihan (1985), p. 23. C.f. Houlihan (1985), pp. 26, Jones / Riley (1985), pp. 19. See e.g. Bowersox / Closs (1996), p. 34, Gattorna / Walters (1996), p. 12, Copacino (1997), p. 7, Simchi-Levi et al. (2004), p. 2.

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today the idea is to consider and manage the entire SC including external business partners as described above. From this perspective, SCM is primarily concerned with establishing a seamless flow of material and information through the entire logistics channel. Stadtler (2005), for example, defines SCM as “the task of integrating organizational units along the supply chain and coordinating material, information, and financial flows in order to fulfil (ultimate) customer demands”.14 The viewpoint that SCM is essentially equivalent to integrated logistics management on an inter-firm level is in part supported in scientific discourses on the nature of SCM. Kotzab (2000) compares the two management concepts and concludes that the difference is very small, if not negligible.15 However, practices and methods proposed within the context of SCM by academia as well as practitioners, often include elements that go beyond what is usually regarded as logistics management. Prominent examples are joint product development between SC partners16 or aligned promotion activities.17 Building on these observations, some authors differentiate between integrated logistics and SCM. They argue that SCM is a broader management concept, for that it is potentially concerned with the integration of all business processes between SC partners, not just logistics activities.18 In the words of Cooper et al. (1997) “SCM ideally embraces all business processes cutting across all organizations within the supply chain”.19 Due to the emphasis of business processes, SCM can also be considered as cross-functional, inter-company business process management.20 An overview of the business processes which can be integrated along the SC is shown in Table 1. Irrespective of its precise definition, the objective of SCM can be summarized by • increasing final customer service, • lowering the amount of resources involved in servicing customers, • and ultimately improving the competitiveness of the entire SC.21

14 15 16 17

18 19 20 21

Stadtler (2005), p. 11. C.f. Kotzab (2000), p. 33. Considered a key issue of SCM by e.g. Simchi-Levi et al. (2004), p. 15. Marketing issues are mainly treated in initiatives between consumer goods manufacturers and retail chains, such as Efficient Consumer Response (see e.g. Kotzab (2001), pp. 29). C.f. Buscher (1999), p. 449, Pfohl (2000), pp. 7, Zijm (2000), p. 323. Cooper et al. (1997), p. 5. C.f. Hewitt (2001), p. 30. See e.g. Cooper / Ellram (1993), p. 14.


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Table 1. Supply chain business processes Business processes along the supply chain Customer relationship management Customer service management Demand management Order fulfillment Manufacturing flow management Procurement Product development and commercialization Source: Cooper et al. (1997), p. 1022

Of course the improved competitive standing of the SC should translate to competitive advantage to all SC members. However, this is not necessarily guaranteed, and must be fostered by appropriate agreements between SC partners (e.g. savings sharing). The major theme to realize the objectives lies, as implied above, in the integration and coordination of the SC and its processes.23 A major question hence is how to actually realize a tighter integration and improved coordination. Noteworthy contributions to this issue are made by Hewitt (1994), Lee (2000), and Bowersox et al. (2000). These authors (independently) propose frameworks for the integration and coordination of business processes along the SC. Based on an empirical study of SC initiatives in practice, Hewitt identifies three dimensions relevant for SC process redesign: work structure, information flow, and decision authority.24 Work structure relates to rearranging and aligning tasks carried out by various parties in a SC. For example, suppliers can take over responsibility for replenishment of the items they deliver. Information flow deals with the availability of data. For one, the speed or timeliness of available information can be increased. In addition, new, formerly unavailable data can be made accessible. Decision authority finally relates to changing decision rights and redesigning decision support systems. Hewitt stresses that truly successful SC initiatives simultaneously address work structure, information, and decision authority which, in summation, results in radically new process design.25 Lee (2000) deals with the question of what constitutes SC integration. As an answer he proposes three dimensions of SC integration: information integration, coordination and resource sharing, and organizational linkage. Informational inte22 23

24 25

A similar compilation of business processes is presented by Buscher (1999), p. 455. See e.g. Stevens (1989), p. 3, Bechtel / Jayaram (1997), pp. 19, Copacino (1997), p. 5, Lee (2000), pp. 31, Stadtler (2005), p. 11. C.f. Hewitt (1994), p. 6. C.f. Hewitt (1994), p. 5.

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gration is viewed as the “foundation of broader supply chain integration”.26 It comprises the exchange of mere data in a first step and knowledge in a second. The latter obviously requires a deeper, trustful relationship. Coordination refers to decision rights, work activities, and resources. The first two aspects are equivalent to the framework by Hewitt, while the last means pooling and sharing of resources by SC partners (e.g. warehouses and other facilities). The organizational linkage dimension deals with the alignment of performance measures and incentives, such as costs, risks, and reward structures. Bowersox et al. develop a so-called “Supply Chain 2000” framework for SC integration.27 It consists of three contexts or components that serve to integrate organizational structures and functional activities: operational, planning and control, and behavioral. The operational context is concerned with the integration of activities within an organization as well as with external business partners. Planning and control embraces sharing of appropriate information, integrated decision making, and alignment of performance measures. The behavioral context deals with the underlying management of relationships to partners. The three frameworks share major characteristics as can be seen from the summarizing overview in Table 2. In result, they make apparent that the integration of business processes along the SC needs to tackle • the work structure (how and by whom processes are operated), • information flows (how and to whom data is communicated), • decision authorities (how and by whom decisions are drawn), • and the underlying relationships between SC partners. Table 2. Dimensions of supply chain integration Hewitt (1994)

Lee (2000)

Bowersox et al. (2000)

Work structure

Coordination and resource sharing

Operational

Decision authority Information flow

Planning and control Information integration Organizational linkage Relational Source: Hewitt (1994), p. 6, Lee (2000), p. 32, Bowersox et al. (2000), p. 72

These principles or dimensions can be used to evaluate and redesign any business process that cuts across the SC. In consequence, a myriad of different change and improvement opportunities can potentially be identified. Nonetheless, common principles or recipes for the integration and coordination of SC processes can

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Lee (2000), p. 33. C.f. Bowersox et al. (2000), pp. 71. The framework was first introduced in the form of a case study in Bowersox et al. (1999), and is also discussed in detail by Stank et al. (2001).


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be drawn from SCM literature. For that purpose, Otto / Kotzab (2001) have analyzed contributions to SCM with respect to underlying (common) principles. The results of their study are presented in Table 3. They are not discussed in detail at this point. Instead they shall give an overview of the common approaches to SC integration as developed in the literature. It should however be noted that SCM does not necessarily aim at a holistic integration of all business processes along the entire SC. Much rather, the appropriate level of integration has to be chosen based upon the specific situation of the SC and its environment.28 Table 3. Principles of Supply Chain Management Principle Compression Acceleration Cooperation Integration Optimization Differentiation / individualization Modularization Leveling Postponement

Explanation Reducing the SC structure (e.g. no. of suppliers) Reducing time lags (e.g. lead times) Enhancing cooperation in planning, control, and operations Reducing time, cost or performance loss at the transition between two processes (e.g. eliminating buffers) Applying quantitative modeling in planning and control Increasing the specification of products / services Reducing time, cost or performance loss of replacing a part of the SC by another (e.g. changing suppliers) Reducing the variation of process parameters (e.g. production volumes) Moving the order penetration point towards the customers

Source: Otto / Kotzab (2001), p. 166

28

C.f. Lambert / Cooper (2000), p. 74, Bask / Juga (2001), p. 139.

12

2.3


Operations Planning in Supply Chains

In the following we turn our attention towards one of the SC business processes as shown in Table 1, namely the manufacturing flow management process. Regardless whether SCM is understood as inter-firm logistics management or a broader management discipline on its own, the flow of material and related information, as well as associated planning and control activities are seen as a core component of SCM.29 This is because operational activities underlying the manufacturing flow directly form the SC’s final output and incur a large portion of total costs and capital needs. Effective and efficient management of operational activities is hence imperative for a SC’s success. The focus herein is not only on manufacturing in a strict sense, but on all processes related to the flow of material, i.e. production, transport / distribution, and storage, altogether subsumed by the general term of operations.30 The coordination of operations along the SC requires well-structured planning processes. In general, planning is defined as a rational, structured decision making process which aims to find the best choice of objectives and measures to a decision situation and its environmental setting.31 The importance of well-planned operations results among others from two characteristics of operational processes. First, they interrelate one with another in many ways. For example, several operations consume identical resources such as production capacity or some processes require the output of others such as component parts needed in final product assembly. Second, operations ultimately serve to cover final customers’ demand. However, as it is usually not possible to initiate all processes upon individual customer orders, expected demands have to be forecasted and anticipated at all tiers of the SC well in time. According to Kansky / Weingarten (1999), the overall task of operations planning in the SC can be seen in deciding on: • when to produce, transport, or store • which quantities of final products, components and raw materials • at which locations in the SC such that customer demand can be met efficiently.32 Of course, this overall problem statement is usually of a daunting complexity and can hardly be tackled by a single, large decision making model that reveals all results on a detailed, implementable level. To make the overall problem yet tracta-

29 30 31 32

C.f. Simchi-Levi et al. (2004), pp. 2, Chopra / Meindl (2001), pp. 6. C.f. Nahmias (1996), p. 1. C.f. Berens / Delfmann (1995), p. 12, Scholl (2001), p. 9. C.f. Kansky / Weingarten (1999), p. 87. See also e.g. Chopra / Meindl (2001), pp. 6.

2.3. Operations Planning in Supply Chains

13

ble, several thrusts on how to deal with it are known in literature and practice and are introduced in the following. The first approach is the typical way of how operations are planned and controlled without much integration of the SC. It is therefore considered only as a benchmark situation prior to the use of SCM techniques. The two approaches presented thereafter are those suggested within the debate of SCM. They are referred to as hierarchical and collaborative planning within the SC. As noted earlier, the latter is the particular subject matter of this work. 2.3.1

Successive and segregated planning

Until recently, the predominant approach to operations planning was the concept of manufacturing resources planning (MRP II). It is implemented in traditional production planning and control systems as well as in more modern enterprise resources planning (ERP) software. Conceptually, MRP II grounds on the logic of successive planning. That is, the overall decision problem is sub-divided into several planning tasks that are executed successively in a hierarchical order. Results from super-ordinate planning levels form given input to succeeding tasks. Master Production Scheduling

Material Requirements Planning

Scheduling

Shop Floor Control

Fig. 2. MRP II planning tasks

The major planning tasks and the corresponding hierarchy are depicted in Fig. 2 and outlined in the following. It should be noted that from a conceptual perspective, the framework can include further planning activities such as medium-term aggregate planning or demand planning.33 However, computerized decision support is usually restricted to the tasks as shown in the figure.34 Master production scheduling serves as the driver within the planning framework. Its purpose is to generate master schedules, i.e. planned production quanti-

33 34

See e.g. Vollmann et al. (1984), pp. 12. C.f. Drexl et al. (1994), p. 1023.

14


ties by period, for final products. Master schedules are obtained by netting demand forecasts and on-hand inventory at the beginning of the planning interval. Material requirements planning (MRP) is the original core element within the concept. Requirements of components and parts are derived from master schedules by a bill-of-material explosion, and lot-sizes are generated based upon some predefined rules such as the EOQ-formula. Initially, only MRP was proposed as a novel, output- or program-oriented planning philosophy in contrast to thus far known inventory control policies.35 The basic idea is to derive dependent demand for parts from final product forecasts rather than from replenishment orders faced at the corresponding stage of the production system. Subsequently, the MRP logic was supplemented by other planning tasks to form the planning framework of MRP II.36 Scheduling serves to generate the order in which individual items are processed on resources such as work centers. Quantities and due dates obtained by MRP are to be obeyed. However, as limited resources availability is accounted for here, capacity shortages can occur, in which case resolutions by plan shifts need to be made. The shop floor control task finally represents the link to plan execution. It includes the release of production orders and subsequent follow-up on progress. MRP II allows a computerized, integrated planning and control of manufacturing processes. As such it was and is widely used in practice since the advent of material requirements planning in the 1960’s. Compared to control concepts known until that time, it brought a new philosophy to plan based on final demand and an increase in shop floor transparency.37 Nonetheless, the concept suffers from considerable shortcomings, especially when it comes to planning with tight capacities and on a SC level. Deficiencies originate for one in its planning logic itself, and second in its limited scope with respect to all operations and planning activities of relevance from a SC perspective. Four major conceptual weaknesses inherent in the planning logic are identified by Drexl et al. (1994). The authors put forward that in MRP II based planning systems • there is no sufficient support of company wide planning embracing various facilities as well as the distribution and sales functions, • plant orders are generated with an isolated view of the item in question, i.e. without taking account of the interdependencies with other items, • average lead times, which include waiting time, are input to the system rather than a result of planning,

35 36 37

C.f. Voß / Woodruff (2000), pp. 180. C.f. Hopp / Spearman (1996), p. 135. C.f. Hopp / Spearman (1996), pp. 105, Kuhn / Hellingrath (2001), p. 121.


15

• and, above all, resource capacities are not systematically considered at all as limiting constraints, except for rough, ex-post capacity checks at the scheduling level.38 The last, major point is amplified by the successive, top-down execution of the planning tasks as indicated in Fig. 2. The approach lacks any anticipative “look forward” or feedback mechanisms that would incorporate consequences of planning decisions on subsequent tasks. The second shortcoming of MRP II, that is its too narrow scope, is already implied by the first point made by Drexl et al. The problem here is that the concept lacks decision support on transport and distribution of intermediate and finished goods as well as on the links between various manufacturing facilities of one company, let alone the entire SC. In result, MRP II like systems are independently operated at various facilities based on locally available data, leading to segregated planning processes along the SC. Coordination can in that way neither be achieved within a single (large) enterprise nor across company borders. As pointed out by Stevens (1989), based on the MRP II concept manufacturing and distribution are effectively decoupled in most companies due to the lack of a coherent integration of planning systems.39 In consequence, it is of little surprise that other, novel approaches to operations planning are proposed within the discussion of SCM. They are the subject of the following sections. 2.3.2

Hierarchical planning

An improved methodology to operations planning in SCs proposed by Drexl et al. (1994), Shapiro (1999), Miller (2002), and many other authors is the concept of hierarchical planning.40 It is also the conceptual framework underlying Advanced Planning Systems (APS), new planning software packages which try to overcome the major flaws known from MRP II. In particular, the objective is to • consider the entire SC, • obey system constraints (e.g. incorporate resource capacities), • and account for the interrelations between distinct processes.41 Hierarchical production planning was first introduced by Hax and Meal (1975) in the form of a case study.42 Since then it received considerable attention in the

38

39 40 41 42

C.f. Drexl et al. (1994), p. 1025. Similar conclusions are given e.g. by Hopp / Spearman (1996), pp. 175, Zijm (2000), pp. 317. C.f. Stevens (1989), p. 7. C.f. Drexl et al. (1994), pp. 1028, Shapiro (1999), pp. 741, Miller (2002), p. 1. C.f. Kansky / Weingarten (1999), pp. 91. C.f. Hax / Meal (1975), pp. 53.

16


literature on production planning and scheduling.43 Its basic idea is in fact similar to successive planning, in that the overall planning problem is decomposed into sub-tasks which interrelate in a hierarchical way. That is, higher level decisions form a given frame for decision making at subordinate levels. This is visualized in Fig. 3 for a hierarchical planning system with two levels. The novelty of hierarchical planning however stems from the fact that the decomposition is regarded as a key aspect in creating a coherent planning system and therefore is based on a careful analysis of the overall decision or planning problem. First, sub-tasks are usually defined such that decisions with similar time horizons and many interdependencies between one and another are combined at one planning level.44 Also, the design of planning levels is oriented on the structure of the organization the planning system belongs to. For example, the number of levels can correspond to the number of layers of managerial decision makers.45 Second, distinct degrees of aggregation are used at the different planning levels. They are chosen in a way to best support the respective decision making processes. For example highly aggregated data is used in long-term, top-level planning, whereas detailed information is used for day-to-day short-term decisions.

Top Level Anticipated Base Level Anticipation (Feed Forward)

Instruction

Reaction (Feedback)

Base Level

Fig. 3. Hierarchical planning system (source: Schneeweiss (1999), p. 19)

Finally, the coupling or interaction of decisions at various levels receives particular attention.46 This is important in order to limit the sub-optimality of the total solution which naturally results from the decomposition of the overall planning problem into smaller chunks. Two concepts can be used to improve the quality of total solutions: anticipation and feedback.47

43

44 45 46 47

See e.g. Stadtler (1988), pp. 36, for a comparative study of various hierarchical production planning systems proposed in the literature. C.f. Kistner (1992), p. 1127. C.f. Scholl (2001), p. 37. C.f. Stadtler (1988), p. 31, Kistner / Switalski (1989), p. 498. C.f. Schneeweiss (1999), pp. 18.


17

Anticipation aims at drawing top-level decisions that do not overly hamper base-level decision making. According to Schneeweiss (1999) it can be defined as “choosing an anticipated base-level and taking into account its impact on the topdecision”.48 This is indicated in Fig. 3 by the “anticipated base level” which becomes a part of the top-level decision situation. To keep the resulting complexity manageable, the anticipated base-level model is usually limited to a rough, strongly simplified representation of the actual base-level objective and decision space.49 Still, even a simplified base-level model is often sufficient to guide toplevel decision making in a beneficial direction. Whereas base-level circumstances directly influence top-level decision making through anticipation, feedback is realized by reporting the consequences of toplevel decisions once they were incorporated into the base-level problem. Feedback communication is indicated in Fig. 3 by the dashed arrow. It can result in a reevaluation of top-level decisions even before the plan is actually put into practice. Alternatively, it may only be used to improve top-level decision making in later, subsequent planning cycles.50 In contrast to the simplified visualization in Fig. 3, hierarchical planning systems usually include more than two levels and comprise more than one separate planning task at a given level. Since there usually are interdependencies between the various planning tasks at one level, coordination among them is required. It is established by the upper level, in that the interrelations are anticipated by the upper level problem. In consequence, instructions received by the various planning tasks are hoped to be coherent one with another.51 This concept, i.e. that coordination is achieved by establishing an all-embracing upper-level, is another key characteristic of hierarchical planning. Nonetheless inconsistencies can arise due to aggregation and coordination problems.52 Aggregation flaws result from the changing level of detail used at different planning levels. Since aggregation usually incurs a simplification of the actual problem structure, it might not be possible to properly disaggregate top-level instructions at the base level. Similarly, coordination defects can occur, since wellcoordinated, aggregate instructions do not necessarily enforce consistency at the detailed, disaggregated level. For example, while weekly production quantities for components and final products are synchronized, they can still become inconsistent on a daily basis after disaggregation in separate planning modules. In order to organize SC operations planning in terms of a hierarchical system, it is useful to consider the various operational activities on the one hand, and differing time frames of decisions on the other as two distinct dimensions. The resulting

48 49 50 51 52

Schneeweiss (1999), p. 18. C.f. Homburg (1996), p. 21. C.f. Stadtler (1988), p. 139. C.f. Kistner / Switalski (1989), p. 480. C.f. Corsten / Gössinger (2001), pp. 34.

18


hierarchical planning system embedded in that framework is shown in Fig. 4, it is the so-called “supply chain planning matrix”.53 Demand planning and fulfillment are the major drivers of all planning decisions, as forecasts and known orders of the SC’s final demand are determined here. Strategic network planning and master planning are two central planning tasks which consider the entire SC, and serve to decide on how expected demand can be effectively satisfied. Herein, strategic network planning is concerned with long-range decisions on the SC’s configuration such as the selection of locations and their capacities. Master planning in contrast operates within the frame defined by strategic decisions, and establishes target quantities, e.g. for production or procurement, on a medium-term, aggregate level for the entire SC such that corresponding demand forecasts can be satisfied. On a short-term level, individual planning tasks are proposed for the different operational processes. Planning decisions comprise order generation for procured material (procurement), lot-sizing, scheduling and shop-floor control (production), and detailed planning of transport flows, tours and truck loads (distribution).54 In fact, multiple instances of these tasks are usually in place dedicated to specific locations or facilities, e.g. individual scheduling systems for each shop floor. A good example of how the various planning tasks look like and interact with each other in practical applications is described by Meyr (2004) for the automotive industry.55 proc urem ent long-term

distribution

sales

Strategic Network Planning Strategic Network Planning

mid-term

short-term

production

Master Planning Master Planning

Material Material Requirements Requirements Planning Planni ng

Dem and Planning

Production Production Planning Planning

Distribution Distribution Planning Planning

Scheduling Scheduling

Transport Transport Planning Planning

Dem and Dem and Fulfilm ent Fulfilm ent

Fig. 4. Supply chain planning matrix (source: Rohde et al. (2000), p. 10)

As discussed above, upper level planning results define the frame for subordinate levels. In particular, the coordination of the various planning modules at the short-term level is established through instructions from their top-level. Therefore, the mid-term master planning plays a crucial role within the framework. It bal-

53

54 55

Rohde et al. (2000), p. 10. Alternative, but similar frameworks are proposed e.g. by Zeier (2001), p. 36, Shapiro (2001), p. 41, Kuhn / Hellingrath (2002), p. 143. For a more in-depth overview of the planning matrix see Meyr et al. (2005), pp. 109. See Meyr (2004), pp. 447.


19

ances supply with expected demand and synchronizes the operational processes across the SC.56 In order to achieve this purpose, it is commonly agreed that it should be organized as a single, centralized planning task embracing the entire SC.57 However given the nature of SCs, centralized decision making is a questionable aspect of the hierarchical planning concept. Concerning strategic network planning one may argue that chances exist to implement it as a single, centralized process, e.g. owned by the most powerful member of the SC, since the planning frequency is low, data is highly aggregate and can even be gathered manually.58 At the master planning level however barriers are higher to centralized decision making across business units or company borders. From a technical perspective, it requires for one a high level of systems integration, as accurate and steadily updated data on all processes must be available. Secondly, the computational complexity grows with an increasing number of facilities and processes covered. Even more important, from an organizational perspective, independent entities in the SC will often resist to open all information to a central planning unit and accept to receive instructions in the form of plan targets. This is further complicated by the fact that individual entities can be involved in SC relationships to several, independent partners as indicated by the example of Fig. 1 above.59 In such a situation it is doubtful, whether an entity can be integrated into centralized planning with one of the SC partners. In result, hierarchical planning can regularly be realized only for a part of the overall SC, e.g. for all processes within one company or business unit. Therefore, the question arises, if there are alternative approaches to coordinate planning of adjacent operational processes without centralized decision making. Such an alternative approach is offered by collaborative planning. 2.3.3

Collaborative planning

Coordination can principally be established in two ways: by a hierarchical (also called vertical) approach or in a non-hierarchical (horizontal) way.60 As we have seen above, hierarchical coordination is achieved through a common top-level decision process which generates synchronized instructions for interrelated subordinate levels from a central perspective. This is a common way to achieve coor-

56 57

58

59 60

C.f. Rohde / Wagner (2005), p. 159. C.f. Corsten / Gössinger (2001), 33, Rohde / Wagner (2005), p. 159, Kuhn / Hellingrath (2002), p. 145. In fact, various successful implementations of SC-wide strategic planning are reported in the literature, e.g. by Lee / Billington (1995), pp. 42, Camm et al. (1997), pp. 128. C.f. Zijm (2000), p. 323. C.f. Brockhoff / Hauschildt (1993), p. 400, Wildemann (1997), pp. 423, Steven (2001), p. 969.

20


dination within companies.61 However, it comes to an end when a joint top-level embracing all interrelating units and their decision processes does not exist and the parties involved cannot agree to establish a central decision maker. In contrast, heterarchical coordination grounds on consensus-like agreements on objectives, measures, and rules between parties with (relatively) equal decision rights. It is usually achieved through communicative, negotiation-like processes.62 In the context of SCM heterarchical coordination of planning tasks is referred to as collaborative planning.63 The term collaborative planning gained popularity due to the industry initiative “Collaborative Planning, Forecasting, and Replenishment” (CPFR). CPFR represents a standardized process for implementing cooperative SC relationships between retailers and manufacturers in the packaged consumer goods industry.64 As implied by its name, the original CPRF model consists of three phases: planning, forecasting, and replenishment.65 Planning here refers to the definition of a cooperation’s mission statement including goals, tasks, and resources, and the development of a joint business plan. The latter specifies the items involved in the cooperation, how they should be marketed, and how their supply should be organized.66 Hence, in this context collaborative planning is understood as business planning, that is as a broad task which specifies how SC partners intend to cooperate. The meaning attributed to collaborative planning throughout this work is different. Here, it is understood as collaborative operations planning, i.e. as a nonhierarchical, cooperative approach to the coordination of operations planning tasks across the SC. To further specify the definition, it is helpful to introduce the concept of planning domains. A planning domain is a part of the SC (including corresponding planning processes) under the control and in the responsibility of one planning organization.67 Examples of planning domains may be the distribution stage of a SC, a regional subsidiary of a large corporation, or the part of the SC which pertains to one company. Planning processes can usually be well-structured and hierarchically coordinated within a planning domain, but are disconnected at the interfaces towards other, adjacent domains. This means, that only rough and uncertain information is available on other domains in the form of demand forecasts (in case of customers)

61 62 63 64 65

66 67

C.f. Brockhoff / Hauschildt (1993), p. 400. C.f. Steven (2001), p. 969, Zäpfel (2001), p. 13. C.f. Zäpfel (2001), p. 13, Kilger / Reuter (2005), p.259. C.f. Ireland / Bruce (2000), p. 83. C.f. Feuerstake (2002), p. 22. See VICS (2002), p. 4, for an overview of the original CPFR model which comprises a total of nine process steps. The model was redefined and partly rephrased by the VICS CPFR committee in 2004; the initial phase is since then called „strategy & planning“, but essentially still consists of the activities described above (see VICS (2004)). C.f. Lohse / Ranch (2001), pp. 58, Seifert (2002), pp. 15. C.f. Kilger / Reuter (2005), p. 259.


21

or supply capabilities (in case of suppliers). Now, collaborative planning is a means to link several such domains and their respective planning processes. Along the lines of Kilger / Reuter (2005) it is defined as follows: “The idea is to directly connect planning processes that are local to their planning domain in order to exchange relevant data between the planning domains. The planning domains collaborate in order to create a common and mutually agreed upon plan.”68 Similarly, Stadtler (2007) defines collaborative planning as “a joint decision making process for aligning plans of individual SC members with the aim of achieving coordination in light of information asymmetry.”69 This is visualized in Fig. 5 for two planning domains. Within each domain hierarchical coordination of planning processes can be realized. Collaborative planning however serves to establish coordination between the domains. The lowestlevel planning task which covers all operational processes within a domain is usually the mid-term synchronization by master planning. Hence, collaborative linkage of domain-specific master planning tasks is of particular interest. Planning Domain 2

Planning Domain 1

Collaborative Planning

Fig. 5. Collaborative planning visualized (source: Kilger / Reuter (2005), p. 259)

A generic collaborative planning process comprises the phases as shown in Fig. 6. Once the cooperative relationship is defined, typical activities follow a cyclical process. Initially, intra-domain plans are generated and relevant data is exchanged between the domains. The crucial phase is then to adjust the internal planning results in an agreed upon way such that a consistent overall plan is obtained and committed to (“negotiation & exception handling”). Thereafter, final results can be executed and resulting performance be measured. The process starts over after a pre-defined re-planning interval. Systems support of collaborative planning, that is support by Advanced Planning Systems (APS), is available for all phases as shown in Fig. 6. Naturally, APS support the generation of intra-domain plans. Regarding data exchange, APS offer

68 69

Kilger / Reuter (2005), p. 259. Stadtler (2007), p. 2.

22


web-interfaces for data visualization and entry by external partners. Also, automatic transmission via XML or e-mail in conjunction with Excel spreadsheets or flat files is available. For example, inventory levels, supply or transport requirements can be transmitted by e-mail to planning partners or accessed through webpages in SAP APO or the SAP Inventory Collaboration Hub.70 Various rules can be defined concerning exception handling. The basic idea here is to monitor some performance indicators such as capacity utilization, order quantities, or service levels. Alerts can then be provided in case predefined value corridors are violated. Workflows specifying how to deal with such violations can be defined, e.g. in the SAP APO Macro Builder.71 In the execution phase, plans are put into practice. It is insofar supported by APS as production, transport, or purchasing orders are created and possibly automatically directed to transactional systems (e.g. a company’s ERP system).

Ex ecu tio n

Definition

Data nge a Exch

Per f Me orman asu rem ce ent

Domain Planning

Ex & ng on ndli i t a tia go n H Ne ptio e c

Fig. 6. Collaborative planning cycle (source: Kilger / Reuter (2005), p. 271)

Finally, performance measurement is too facilitated by APS in that key performance indicators can be defined and kept track of in so-called plan monitors. Performance measurement can relate to plan figures, actual data from past periods, or comparisons of plan and actual figures. Despite these extensive support functionalities, a shortcoming to date is that only little decision aid is provided with respect to the negotiation process itself. Here, the question of which tools to utilize and how to embed their use in the entire collaborative planning process as depicted above is largely unanswered, and it is left to the individual user or implementer to define the workflows associated with alerts or violations as explained above. It is therefore the purpose of this work to develop a negotiation-based collaborative planning scheme that goes beyond mere data exchange and to demonstrate which improvements in SC performance can result from its application.

70 71

C.f. Bartsch / Bickenbach (2002), pp. 361, Kilger / Reuter (2005), p. 276. C.f. Kilger / Reuter (2005), p. 277.


23

A final note is in place on the applicability of collaborative planning in SC relationships. As described above in 2.1, SCs usually are complex networks comprising a number of companies, facilities, and often thousands of stock-keeping units. As collaborative planning requires substantial investments in hard (e.g. IT systems) and soft matters (e.g. team building across companies), it is clear, that it cannot realistically be implemented between all planning domains of a SC. Following Williamson’s (1985) classification of transactions by frequency and degree of asset specificity, Skjoett-Larsen et al. (2003) suggest that so-called developed or advanced CPFR (i.e. a close collaboration) should be used where transactions recur frequently and require at least some specific investments by the trading partners,72 which “lock” the SC members into a supply relationship and create barriers to switch suppliers or customers easily. Products or components requiring such dedicated investments are usually the major items dealt with in a SC (by volume and / or contribution to the value / functionality of the end-product). Specific investments around such items are often joint R&D and development actitivities which e.g. ensure, that parts fit together appropriately, can be processed in the desired way, or provide customized end-customer functionality. Even when only key items and their corresponding planning domains are regarded as candidates for collaborative planning, additional factors can come into play, which foster or inhibit the applicability of collaborative planning. Based on a survey by Barratt (2004), these mainly go back to the relationship and cultural fit between the respective SC members. Enablers of collaborative planning are personal relations across various levels and functions of the companies, mutual interdependence, openness, and (at the base) the right individual chemistry. Inhibitors on the other hand are mechanistic behavior, functional (silo-oriented) management styles, and a lack of honesty, trust and process visibility.73 Only when sufficient “enablers” are in place, collaborative planning will likely be implemented successfully. Finally, as in any SC integration project, expected benefits of collaborative planning have to be compared with the cost of initial implementation and ongoing operation of the process.74 McLaren et al. (2002) and Kilger (2005) give indications on the potential benefits (e.g. financials, service levels, as well as qualitiative factors such as improved market knowledge) and costs (system implementation and integration, process coordination costs, data translation and integration, switching costs, etc.).75 Only when expected benefits of developing and implementing a collaborative planning process exceed associated costs, an implementation can be recommended.

72 73 74 75

C.f. Skjoett-Larsen (2003), p. 538. See Barratt (2004), pp. 81, for a full overview. C.f. Kilger (2005), pp. 281. C.f. McLaren et al. (2002), pp. 355, Kilger (2005), pp. 291.

24


Recommended readings • Simchi-Levi, D. / Kaminsky, P. / Simchi-Levi, E. (2004): Managing the Supply Chain – The Definitive Guide for the Business Professional, 2nd edition, Boston et al. 2004 (especially chapter 1 “Introduction”). • Meyr, H. / Wagner, M. / Rohde, J. (2005): “Structure of Advanced Planning Systems”, in: Stadtler, H. / Kilger, C.: Supply Chain Management and Advanced Planning – Concepts, Models, Software and Case Studies, 3rd edition, Berlin et al. 2005, 109-115. • Kilger, C. / Reuter, B. (2005): “Collaborative Planning”, in: Stadtler, H. / Kilger, C.: Supply Chain Management and Advanced Planning – Concepts, Models, Software and Case Studies, 3rd edition, Berlin et al. 2005, 259-278.

3 Modeling Framework and Relevant Literature Content This chapter sets out a quantitative modeling framework for the following treatment of collaborative planning and reports on findings from literature related to the problem setting. In section 3.1 we outline the planning situation considered here and describe mathematical programming type models which can be used for planning purposes within single planning domains. Furthermore, links to other planning domains will be modeled by additional constraints. Section 3.2 contains a brief literature review on the value of information sharing and collaboration between SC partners. It casts some light on what can be gained from closer collaboration. Finally, in section 3.3 we review and comment on approaches proposed in the literature to achieve coordination of planning between independent domains. Key points • Mathematical programming models are well suited for collaborative planning at the master planning level; the multi-level capacitated lot-sizing problem (MLCLSP) is a good representative model which plans material flows over multiple tiers taking into account limited resource capacities and fixed setup/ order costs • Information sharing and integration increase the efficiency of SC operations, especially when the SC is complex (e.g. deals with multiple products and tiers and capacities are limited) and a high portion of costs accrues at upstream tiers – the benefit strongly depends on how additional information is utilized • Approaches to coordinate planning across independent domains proposed in literature are rather hierarchical (i.e. give more decision authority to individual players) and require a relatively high level of integration (i.e. sharing a sensitive information)

3.1

Modeling

3.1.1

Decision situation and modeling assumptions

In terms of the planning level, the focus of this work lies on the mid-term coordination of operations by master planning (MP). In the traditional production planning framework, MP has its origins in Aggregate Production Planning and, as implied by its name, Master Production Scheduling.76 Hence, the purpose of MP, as far as it concerns production processes, is to specify production and shipment rates 76

See e.g. Silver et al. (1998), pp. 538, Chase et al. (1998), pp. 552, Vollmann et al. (1984), pp. 12.


26

3. Modeling Framework and Relevant Literature

as well as capacity adjustments for plants such that expected customer demand can be satisfied efficiently.77 The underlying planning horizon covers a medium term of 3 to 18 months (depending on the problem setting) and is usually subdivided into weekly or monthly time buckets. Due to the shift of focus towards SCs, the goal of MP is however broadened, for that it seeks to synchronize all operational processes along the SC or, given our discussion in 2.3.2, at least within the planning domain under consideration.78 In order to do so effectively, it needs to account for interdependencies between the various processes. Suppliers

Production facilities

Distribution facilities

Customers

Fig. 7. Logistical network structure (source: with adaptations from Thorn (2002), p. 31)

A typical logistical network considered in MP contains the elements as shown in Fig. 7. Procured input materials are supplied by external vendors which are not part of the planning domain. The domain’s output is created by a network of plants, potentially in a multi-stage manner linked by internal supply relationships. Final products are shipped through the distribution system (also potentially multistage) to the domain’s final customers. Building upon Fig. 7, the decisions of MP are described in Table 4. In order to ensure feasibility of planning results, it is important that all decisions are consistent with each other and in line with relevant constraints. To maintain consistency it is necessary to capture the interrelations between individual processes. For example, if input materials are needed for production, production levels must be in line with the availability of supplied material. Likewise distributed quantities must be based on what is actually planned for production, etc.

77 78

C.f. Silver et al. (1998), pp. 556, Stadtler (2000a), p. 11. C.f. Rohde / Wagner (2005), p. 159.

3.1. Modeling

27

Table 4. Basic decisions of master planning Decision type

Description

Procurement Quantities of input materials purchased from external suppliers Production / material Production and handling quantities, or output levels of other handling relevant operational processes Inventories Inventory levels at the end of planning periods Customer shipments Quantities supplied to customers and their origins Transports Transport quantities on all transport links considered Source: Rohde / Wagner (2005), pp. 159

System constraints mainly concern available resource capacities and other technological restrictions (e.g. the assignment of products to plants). They describe the configuration of the network and are largely a result of Strategic Network Planning, as explained above in 2.3.2. However, as far as they can be influenced at a mid-term level, adjustments of resource capacities can also be a part of MP and form a second set of decisions which go beyond what is presented in Table 4. For example, working times/ shifts or transport capacity reservations at third-party carriers can be adjusted on a medium term. The formal objective underlying MP decisions is usually a financial measure. Chopra / Meindl (2001) define it as “to satisfy demand in a way that maximizes profit for the firm”.79 When all demands are supposed to the covered, revenues are fixed and profit maximization is equivalent to minimizing the cost of supplying the demand. Alternatively, one may try to maximize net revenues, i.e. gross revenues less those costs of supply that are influenced by the planning decisions. However, since cost minimization and net revenue maximization can be converted one to the other, we focus only on cost minimization in the following.80 Principally, other objectives can be regarded, too, such as time-oriented or resource-oriented measures, e.g. on-time deliveries or capacity utilization.81 However, since cost rates measure the economic effort required for the various operational processes in common units, they allow for proper tradeoffs between planning decisions.82 Therefore, they form the best basis to direct planning decisions and are used as the only objective, here. Relevant types of costs are those associated with the planning decisions as described above, i.e. procurement, production and handling, inventory, distribution, and transport costs. As far as capacity adjustments are possible, corresponding costs have to be considered, too. Finally, if demand partially needs not to be cov-

79 80

81 82

Chopra / Meindl (2001), p. 103. Minimizing cost is equivalent to maximizing net revenues when missed revenues are considered as costs and the degree of demand satisfaction as a variable to be decided upon during planning. For an overview of other potential objectives see Thorn (2002), pp. 34. It is e.g. difficult to balance on-time delivery and capacity utilization, unless these measures are expressed in terms of costs.

28


ered or can be shipped delayed, costs of lost sales and / or backorders must be included for proper tradeoffs with remaining planning alternatives. Medium term planning does not require to consider processes, materials, and resources in full detail. In fact, a detailed perspective (e.g. based on individual stock-keeping-units) is usually neither realizable due to the problem size nor practicable. In order to keep the problem manageable and obtain meaningful results some aggregation is required. For example, families of final products are used which comprise items with similar demand patterns and resource needs.83 Similarly, plants or plant segments (e.g. manufacturing lines) are used as resources instead of individual work centers, flow lines stations etc. Moreover, not all resources and processes have to be considered. The focus should be on operations which potentially form bottlenecks or incur high costs so that an efficient utilization is imperative. Once planning decisions for the critical processes have been established, the consequences for all remaining operations can be derived in a following step. Given the various types of decisions and associated cost tradeoffs as well as the system constraints, it is obvious that MP usually deals with a complex decision situation. Finding a good, not to say the best, set of consistent decisions is a daunting task. Therefore, quantitative models are useful to support decision making. Based on the problem description, mathematical programming models (MPM) are most suitable for this purpose. As pointed out by Shapiro (1999), MPM are “the only analytical tools capable of fully evaluating large numerical data bases to identify optimal, or demonstrably good, plans”.84 In contrast to other analytical methods85 MPM are not only able to cope with the large number of alternative decisions, but also help identifying the best set of those. As with any analytical method, using MPM of course relies on some simplifying assumptions. The major simplifications are referred to as proportionality, additivity, divisibility, and certainty,86 and are shortly discussed in the following. Proportionality stands for the fact that any decision variable’s contribution to the objective function and to all constraints is proportional to the variable’s value. In our problem’s context this means that costs associated with operations grow proportionally with output levels, and that per unit input and resource needs are fixed. Additivity implies that every function within the model equals the sum of individual contributions of the respective decisions. For example, total cost follows as the sum of the costs for each of the operations considered, total usage of a resource as the sum of resource needs by individual operations etc. Divisibility re-

83

84 85

86

C.f. Hax / Meal (1975), p. 55, Stadtler (1988), p. 83. For an example method of how to compress product-process structures based on resource requirements see Billington et al. (1983), pp. 1132, and Stadtler (1998), pp. 178. Shapiro (1999), p. 740. E.g. simulation models (see Thorn (2002), pp. 49, for an overview of simulation model applications to planning in supply chains). C.f. Hillier / Liebermann (2001), pp. 36, Shapiro (2001), pp. 84. For a brief overview of mathematical programming see e.g. Stadtler (2005b), pp.473.

3.1. Modeling

29

fers to the assumption that variables can take any fractional value and only applies to linear programming (LP) models. Besides linear variables we also allow for binary variables with 0-1 values. With binary variables present, the programming model becomes a mixed-integer model. Finally, certainty means that all parameters are deterministic constants. In our context this implies that all input data such as per unit costs and resource needs are known with certainty. Assessing the applicability of the simplifying assumptions, one can state that assuming linear and additive relationships certainly is a simplification from real world relationships. On the other hand, it is a close-enough approximation for many functional relations such as between operation levels and associated costs or resource requirements. Also, the divisibility of linear variables is mostly uncritical, as rounding off resulting values does usually not affect the overall result too much. This holds true, as long as binary variables are added and used in situations, when discrete “go” / “no go” decisions have a major impact on the model’s solution. Whenever a discrete decision of this kind notably affects costs or system constraints, the divisibility assumption gives a too optimistic picture of the situation, because here rounding off is only possible to integer 0-1 values and does have a major impact on the overall result. Therefore, binary variables and hence mixed-integer models have to be used whenever discrete decisions play an important role, e.g. when production setups with fixed costs are considered. Finally, a questionable assumption is the certainty property. Clearly, some randomness is present in any real-world process, so that it cannot be perfectly described by a deterministic model. On the other hand, just as with the linearity assumption an abstraction from stochastic variations is often permissible, as long as the variations stay within some limits. In fact, as mentioned by Rohde / Wagner (2005), “reasonable results can only be expected for production processes having low output variances”. 87 Otherwise, planning results quickly become obsolete, turning planning to a rather useless effort. Given a medium term planning horizon of several months, reality will however always deviate from planning assumptions. This especially concerns demand forecasts, but also other events such as machine breakdowns can cause considerable changes to what was initially expected. In order to deal with this uncertainty and still make use of MPM, the standard procedure is periodical re-planning based on a rolling horizon basis.88 As demonstrated in Fig. 8, a plan covering T periods is only partially implemented (say for Ti periods). Thereafter a new planning cycle is initiated based on updated information. The fact that plans are regenerated on a rolling basis also brings some interesting consequences for collaborative planning between individual domains. This will be dealt with in more detail later on in chapter 5.

87 88

Rohde / Wagner (2005), p. 160. See e.g. Fleischmann et al. (2005), pp. 83.


30

1

Ti

T Ti+1

T+Ti

Fig. 8. Planning with rolling horizons (source: Fleischmann et al. (2005), p. 84)

3.1.2

Intra-domain planning model

Several authors have developed mathematical programming models for planning of operations at the master planning level, which are briefly discussed in the following. Thereafter we present the model which is used for intra-domain planning in this work and forms the basis of the collaborative planning scheme developed in later chapters. It is based on the literature findings reported first. An overview of the contributions regarded here and their characteristics is given in Table 5. Of course, the compilation in Table 5 is not exhaustive. In particular, contributions which date back further and where not specifically published under the theme of SCM are not included, although they may deal with a decision situation and model similar to what we consider here.89 To avoid a lengthy elaboration on each of the models, only the major commonalities and differences are outlined. All MPM mentioned in Table 5 depict a decision situation as described in the previous section. In essence, they cover a finite planning horizon of T consecutive periods, consider several final products, and a multi-level structure of processes linked by balance equations. Also, limited resource capacities for production, and partly also for distribution and procurement processes are included as constraints. As explained above, the objective function regularly consists of minimizing total costs or, in some cases, maximizing net revenues. Differences between the models occur with respect to their scope, possible adjustments of resource capacities, and discrete decisions.

89

Interested readers are referred to the review articles by Bhatnagar et al. (1993), Thomas / Griffin (1996), and Erengüc et al. (1999) for a comprehensive overview. A more detailed comparative study of recent models is given by Thorn (2002), pp. 103.

cost min

net rev. max,

prod., distr.

proc., prod., distr.

prod., distr.


prod.



proc., prod.

prod., distr.

prod., distr.

Özdamer / Yazgac (1999)

Escudero et al. (1999)

Barbarosoglu / Özgür (1999)

Zäpfel / Wasner (2000)

Ertogral / Wu (2000)

Haehling v. L. / Pilz-Glombik (2001)

Thorn (2002)

Rota et al. (2002)

Karabuk / Wu (2002)

Jung et al. (2005) cost min

target utilization

net revenue max

net revenue max

cost min

cost min

cost min

cost min min. utilization

cost min

cost min

prod., distr.

Erengüc et al. (1999)

Objective Fct.

Scope

Contribution

balance eq., capacity











Constraints

-

-

prod. setups

-

transp. setups

prod. setups

transp. setups

prod. & transp. setups

-



Discrete Decisions

-

outsourcing, under- / over utilization

-

-

type & no. of transport vehicles

type & no. of transport vehicles overtime production

-

-

no. of transport vehicles

over-/undertime prod.

Capacity Adjustments

3.1. Modeling

Table 5. Overview of mathematical programming models 31

32


Scope here relates to the number of stages of the logistical network according to Fig. 7 that are included in the model. The most extensive models are designed to cover procurement, production, and distribution processes. These are the contributions by Escudero et al, Zäpfel / Wasner, Haehling von Lanzenauer / PilzGlombik, and Thorn. Others take a more limited view of only a part of the potential processes. Erengüc et al., Özdamar / Yazgac, Barbarosoglu / Özgür, Karabuk / Wu, and Jung et al. consider production and distribution activities, whereas Rota et al. concentrate on procurement and production. Ertogral / Wu focus on production processes. Adjustments of resource capacities are permitted as additional planning decisions by some authors. Potential overtime for production processes is considered by Erengüc et al. and Ertogral / Wu. Karabuk / Wu allow outsourcing, i.e. external supply of final products, to cover demand peaks. Özdamar / Yazgac, Zäpfel / Wasner, and Haehling von Lanzenauer / Pilz-Glombik restrict production capacities to fixed values, but include planning decisions on type and number of vehicles to be used on transport links in the respective planning periods. Considerable differences relate to the type of discrete decisions included in the models. No such decisions at all are regarded by Escudero et al, Thorn, and Jung et al. The resulting models therefore are pure linear programs. Most other authors incorporate discrete decisions. Binary setup decisions in production and / or transportation are considered by Erengüc et al., Barbarosoglu/ Özgür, and Ertrogral / Wu. Özdamar / Yazgac, Zäpfel / Wasner, and Haehling von Lanzenauer / Pilz-Glombik go even further and model their transport decisions by integer variables which can take values other than 0 and 1.90 A special note is needed for the model of Karabuk / Wu, as its objective function contains a quadratic term for deviations of target utilization levels. Moreover, the model is a stochastic program, i.e. is based on a set of scenarios for final demand, which maximizes the expected net profit across them. In summary, it becomes clear that the models differ in varying degrees from one and another. These differences are however rather due to the specific SC setting considered by the various authors than to a truly differing modeling approach. In fact, they all share a common, principal structure: material flows planned to satisfy final demand are captured by balance equations and restricted by available resource capacities. Since it is not the purpose of this work to develop yet another (problem specific) model, we assume one of the models mentioned above to be used for planning within planning domains. In choosing the model we follow the example of Ertogral / Wu. The model they use is the multi-level, capacitated lot-sizing problem (MLCLSP). This choice is motivated by the fact that the MLCLSP is a standard problem which is well known and documented in literature. Moreover, it captures the essential planning issues presented above: several final products, a multilevel process structure, limited capacities, and discrete setup decisions.

90

Of course, these formulations can be redefined to contain only binary variables. However, this comes at the expense of a larger number of binary variables.

3.1. Modeling

33

Also, it should be noted that the collaborative planning scheme developed in later chapters is not specifically tailored to the MLCLSP as planning model within each domain. Therefore, our selection of the MLCLSP as intra-domain planning model serves more as the choice of a representative example than as a limitation to this specific problem situation. In its basic, so-called I&L version,91 the MLCLSP can be formulated as follows.92 Model 1. MLCLSP Indices t planning period 1…T j operation / item ∈ J r resource ∈R Index sets / boundaries T planning horizon J set of operations / items R set of resources set of direct successor operations of j Sj Data chj unit holding cost of operation j cfj setup cost associated with operation j unit cost of overtime at resource r cor Ej,t (external) demand for operation j in period t capacity of resource r in period t Cr, t Lj,t maximum lot-size constant for operation j

X j, t / X j, t upper / lower bound on output level of j in period t I j, t / I j,t

upper / lower bound on inventory level of j at the end of period t

O m,t / O m,t upper / lower bound on overtime on resource r in period t ar,j rj,k Variables c xj,t ij,t yj,t or,t

91

92

unit requirement of resource r by operation j unit requirement of operation j by successor operation k total cost output level of operation j in period t inventory level of operation j at the end of period t setup variable of operation j in period t overtime at resource r in period t

“I&L” abbreviates “inventory & lot-size” and means that end-of-period inventory levels and lot-sizes are directly used as decision variables (c.f. Stadtler (1996), p. 562). C.f. Tempelmeier (2003), pp. 209, Günther / Tempelmeier (1997), p. 183, Stadtler (1996), p. 562. Please note that the formulation considered here neglects setup times (for the inclusion of setup times see e.g. Tempelmeier (2003), p. 209).


34

Formulation

min c s.t.

T

c=∑

(1) (2)

T

∑ (ch j i j ,t +cf j y j ,t ) + ∑ ∑ cor or ,t

t =1 j∈J

t =1 r∈R

∑ r j ,k xk ,t + i j ,t

∀j ∈ J , t = 1..T

(3)

∀r ∈ R, t = 1..T

(4)

∀j ∈ J , t = 1..T

(5)

∀j ∈ J , t = 1..T

(6)

I j , t ≤ i j ,t ≤ I j , t

∀j ∈ J , t = 1..T

(7)

O r , n,t ≤ or , n,t ≤ O r , n,t

∀r ∈ R, t = 1..T

(8)

y j ,t ∈ {0,1}

∀j ∈ J , t = 1..T

(9)

i j ,t −1 + x j ,t = E j ,t +

∑ ar , j x j , t

j∈J

k∈S j

≤ Cr ,t + or ,t

x j ,t ≤ L j , t y j , t

X

j ,t

≤ x j ,t ≤ X

j ,t

The model plans output (xj,t) and inventory levels (ij,t) of all operations considered as well as expansions of resource capacity (or,t). Operations can principally represent production, transport or other value-adding operational activities. The objective function minimizes the value of variable c which, due to constraint (2), represents the total cost incurred from setups, inventory holding, and capacity expansions.93 Constraints (3) capture the flow balance between output, inventory and consumption by (external) customer demand Ej,t or successor operations.94 Constraints (4) represent capacity restrictions, while lot-sizing relationships are expressed in (5). Constraints (6) through (8) specify lower / upper bounds on variable values, as far as this is necessary. Assigning total cost to the extra variable c is not strictly required at this point, but will prove handy in later sections. As demonstrated by Stadtler (1996), there are more efficient formulations of the MLCLSP in terms of the integrality gap of the lp-relaxation and thus in terms of solution time.95 However, for the sake of simplicity and clarity we only deal with the basic I&L formulation throughout this work.96

93

94

95 96

Variable operation cost rates are assumed constant over the planning interval and thus omitted. It should be noted that without loss of generality replenishment lead times are neglected (i.e. assumed as zero). Although any fixed multiples of the planning period lengths could be used instead, this is omitted for ease of exposition. C.f. Stadtler (1996), pp. 575. Also, integrality gap and branch-and-bound solution time of the I&L formulation can be considerably reduced by strong valid inequalities as proposed by Pochet / Wolsey (1995), p. 273.

3.1. Modeling 3.1.3

35

Modeling links to adjacent planning domains

The above model depicts the isolated perspective of a single planning domain facing only external (market) demand. However, in order to realize collaborative planning it is important to explicitly regard the links to other (partnering) planning domains because the local planning situation depends on planning results of these domains, and vice versa. A planning domain can have direct links to two types of partners: customer and supplier domains. The situation is visualized in Fig. 9. It shows the part of the SC under the control of the domain under consideration (referred to as “local domain”) and corresponding planning processes. Now, the domain’s final output may be dedicated to either external customers, i.e. customers that cannot be directly influenced in what they demand, or to SC partners, i.e. customers that are able and willing to cooperate. These customers control another, more downstream part of the overall SC (referred to as “customer domain”) and corresponding planning processes. The link to a customer domain is established by order requirements requested by the customer based on the demand he faces. Similarly, the local domain usually needs supplies by vendors. To some vendors only market relationships may exist. However, others may be cooperative SC partners. The more upstream part of the SC which is controlled by a partnering supplier is called “supplier domain”. The link to a supplier domain is expressed in terms of supply requirements requested by the local domain as shown in Fig. 9. In what follows we specify the links to customer and supplier domains as additional constraints which can be added to the intra-domain planning model. The additional data items, decision variables, and constraints required to model thev links are presented in turn for the supplier and customer domain. Supplier Domain

Local Domain

Supply requirement s

Cust omer Dom ain

Order requirement s

Ext ernal dem and

Fig. 9. Links between planning domains Extension 1.1. Links to supplier domains Index sets JS set of supplied items (operations) Data XSj,t proposed supply quantity of j in period t IS j, t / IS j, t upper / lower bounds on supply inventory of j at the end of period t

Ext ernal dem and

36


Variables xsj,t (assumed) supply quantity of j in period t isj,t supply inventory of j at the end of period t Formulation

s.t.

T

c=∑

∑ (ch j i j ,t

t =1 j∈J

is j ,t −1 + xs j ,t =

T

+cf j y j ,t ) + ∑

T

∑ cor or ,t + ∑ ∑ ch j is j ,t

t =1 r∈R

∑ r j ,k xk ,t + is j ,t

t =1 j∈JS

∀j ∈ JS , t = 1..T

k∈S j

(10) (11)

xs j ,t = XS j ,t

∀j ∈ JS , t = 1..T

(12)

IS j, t ≤ is j ,t ≤ IS j, t

∀j ∈ JS , t = 1..T

(13)

Constraints (10) through (13) can be used in two ways. Assuming that the supplier has announced supply proposals XSj,t, these can be added to Model 1 as presented above in order to find the optimal intra-domain plan given supply quantities XSj,t ((10) replaces the original cost function of (2)). Proposed supply quantities by period XSj,t are input to the model due to constraints (12). Balance equations (11) link supplies to their consumption, thereby restricting internal operations by the availability of supply items. However, inventory holding of supplied quantities is permitted, in order not to fully dictate internal operations by supply quantities. Consequently, the cost function in (10) is enhanced by inventory holding costs of supply items. Even though these costs may in fact be covered by the supplier, their inclusion is important for ensuring a proper balancing between supply inventory holding and the remaining operations. Constraints (13) specify boundaries on the supply inventory isj,t, if this is required. Alternatively, when no supply proposals are known, constraints (12) can be skipped. In this case supply quantity variables xsj,t can take any desired value, and no inventory holding in the form of isj,t will occur. In this mode, constraints (11) reveal supply quantities (resulting values of xsj,t) that have to be requested from the supplier in order to make the resulting plan realizable. The situation is similar for the customer domain. Extension 1.2. Links to customer domains Index sets / boundaries JO set of order items (operations) Data XOj,t proposed order quantity of j in period t Variables xoj,t order quantity of j in period t Formulation i j ,t −1 + x j ,t = E j ,t + xo j ,t +

xo j ,t = XO j ,t

∑ r j ,k xk ,t + i j ,t

∀j ∈ JO, t = 1..T

k∈S j

∀j ∈ JO, t = 1..T

(14) (15)

3.2. Benefits of Information Sharing and Collaboration

37

Assuming that the buyer has announced order proposals XOj,t, constraints (14) and (15) can be used to incorporate the order quantities into the intra-domain planning model and generate the optimal plan given the proposed pattern of orders. Constraints (14) replace the original flow balance equations (3) for all items ordered by a buyer, so that two sources of demand are considered: (anonymous) demand by external customers Ej,t and orders by the collaboration partner(s) xoj,t. If no order quantities are known from the buyer, (15) can be skipped, and the extended model can be used to generate a proposal of supply quantities (resulting values of xoj,t). However, for doing so lower and upper bounds on xoj,t must be specified at a minimum, otherwise the values of xoj,t would be zero in the optimal solution. This aspect is discussed in greater detail below in chapter 4. In terms of modeling, the situation is equivalent for all planning domains joining the collaborative planning process. Only the question of who is viewed as customer or supplier depends on each planning domain’s local perspective. Thus, vendor orders generated at one domain, e.g. by adding constraints (11) to the intradomain model, become customer order requests XOj,t, once they have been communicated to the supplier domain. This makes clear that synchronized planning results for all domains can only be obtained through a well structured coordination mechanism. Coordination schemes which are proposed in the literature and applicable to this decision situation are discussed in section 3.3. Beforehand we briefly touch upon the question of what can be gained from closer collaboration in planning of SC operations.

3.2

Benefits of Information Sharing and Collaboration

Without any coordinating action domain-specific plans are generated with an isolated view of the domain in question and based on local information only. If mathematical programming models are used for planning purposes as described in the previous section, a local demand forecast (for the final output of a given domain) must be available and serves as the major driver of planning decisions. Interactions with other domains are simply ignored. However, as pointed out in section 2.3, purely isolated planning and operation of individual domains results in sub-optimization of the SC as a whole and inefficiencies such as high inventory buffers or frequent plan adjustments. Collaborative planning tries to eliminate this inefficiency and thereby to improve the SC’s performance. An important issue herein is to understand the benefit of increased SC integration. To give an idea of what can be gained from collaboration, some findings from literature are reported in the following and transferred to the problem setting considered here. Objects of information sharing and collaboration considered in the literature are operating characteristics and policies on the one hand, and demand forecasts on

38


the other. Since demand forecasting is not the major concern of this work, articles dealing with collaborative forecasting are not cited in what follows.97 Articles assessing the value of information sharing usually are based on simple, stylized SC settings. Mostly two partners (a retailer and a supplier), a single product, and random demand with a known distribution are considered. The SC operates by inventory control policies which trigger replenishment decisions. In order to explore the impact of information sharing, usually a traditional setting with local information for each partner and a new setting with improved information and synchronized operating rules are analyzed. It should be apparent that additional information is always beneficial, i.e. decisions made with more information cannot be worse than those based on fewer data.98 The goal of the contributions is to demonstrate ways of how to exploit additional information and to quantify the potential benefits. Bourland et al. (1996) analyze the effects of timely demand information in a two-partner SC where both parties use fixed replenishment periods which are offset by a given time interval. For example, the retailer orders every Monday while the supplier triggers production every Wednesday. They analyze the advantage of communicating actual demand at the retailer which occurred after his last order but before the supplier’s production quantity decision. Since this demand influences the retailer’s next order decision, knowledge of the demand is advantageous to the supplier. Bourland et al. find that sharing the demand information results in lower inventory holding and increased service level at the supplier. The benefits are significant when demand variability is high and the replenishment period offset is large relative to the cycle length: e.g. inventory reduction of 26% and fill rate increase from 92 to 96% with demand coefficient of variation of about 0.33 and an offset of almost the cycle length (19 vs. 20 periods).99 Chen (1998) considers a multi-tier, serial SC where replenishments are made in multiples of a base batch size. He compares operating costs of reorder point policies. In one setting, the reorder point policies are based on installation stock, i.e. the local inventory position at each tier, whereas in the other echelon stock policies are used. The second setting requires knowledge of system-wide inventory downstream from each echelon. In a computational study Chen observes cost reductions of 0 to 9.75% from using echelon reorder point policies, on average costs decrease by 1.75%. The benefit (percentage cost reduction) of echelon reorder points grows with the number of tiers in the SC and the length of replenishment lead times between adjacent tiers.100 Gavirneni et al. (1999) study a two-tier SC with fixed capacity at the supplier. When production orders exceed capacity, a costly expediting (overtime) mode is used for production. Both parties use (s,S) order-up-to policies for inventory con-

97

98 99 100

Interested readers are referred e.g. to Aviv (2001), Thonemann (2002), Zhao et al. (2002), and the references discussed there. C.f. Gavirneni et al. (1999), p. 20. C.f. Bourland et al. (1996), p. 250. C.f. Chen (1998), pp. S231.


39

trol. Three settings are analyzed: a traditional one with no information sharing, one with sharing of system parameters, i.e. cost rates, demand distribution, control policies and parameters, and one with sharing of actual demand data in addition to the system parameters of setting two. Cost results obtained with setting three always outperform those of setting two, which in turn outperform results of setting one. The gain between setting one and two is substantial with average savings of around 50%. Costs of setting three compared to setting two are lower by 1 to 35% depending on system parameters like supplier capacity and cost rates. Gavirneni (2002) deals with the same problem but proposes to modify the operating policy, such that the retailer is forced to place orders whenever cumulative demand since his last order exceeds a given level δ. The order quantity is not known to the supplier in advance, but yet some uncertainty is removed from the system.101 As a result, total SC operating costs are reduced through the new policy on average by 10.5% compared to the third setting in Gavirneni et al. (1999). The author therefore concludes that additional information can be better utilized by appropriately changing the operating policies as opposed to simply adjusting parameters of existing policies.102 Cachon / Fisher (2000) consider a SC with one supplier and N identical retailers. Replenishments take place in multiples of a base batch size and based on reorder point policies. They compare a traditional setting with local information to a setting where the supplier has access to the retailers’ inventory positions. Computational results show an average cost reduction vs. the traditional setting of 2.2%. On the other hand, reductions of the shipment lead time or the base batch size by about 50% lead to cost decreases of 21% and 27%, respectively.103 The authors conclude that for the model studied, improvements of operating characteristics such as lead time and batch size reductions boost performance more than mere exchange of information.104 Finally, Lee et al. (2000) study a 2-party SC with order-up-to policies in place at both, the retailer and the supplier. However unlike to other contributions, their model assumes that the retailer’s demand is auto-correlated over time. That is, a period’s demand is partly influenced by the demand of the pervious period.105 They too study two settings, one with local information and one where the supplier has knowledge of final demand. Approximate analytical results as well as simulation runs suggest significant inventory and cost reductions for the supplier with availability of demand data. The benefits increase with growing degree of autocorrelation, demand variance, and length of replenishment lead time.106 However, their results are somewhat expelled by Raghunathan (2001) who comments on the article by Lee et al (2000). He points out that their results depend on the

101 102 103 104 105 106

C.f. Gavirneni (2002), p. 645. C.f. Gavirneni (2002), p. 651. C.f. Cachon / Fisher (2000), pp. 1044. C.f. Cachon / Fisher (2000), p. 1046. C.f. Lee et al. (2000), p. 628. C.f. Lee et al. (2000), pp. 635.

40


fact that in the local information setting the supplier forecasts future demand based only on the most recent retailer order. If he used the entire order history, the value of shared demand information would be smaller, and in fact would converge to zero in the long run.107 This is because the order history can be used to appropriately forecast future demand given the autocorrelation of the demand process. The above contributions show that there is no common answer to the question of what can be gained from information sharing and closer collaboration. Much rather, resulting benefits depend on the problem setting or model studied and the type of analysis proposed by the authors. Nonetheless, some common observations can be extracted. First, as stated by Gavirneni et al. (1999), additional information is always beneficial as it allows better decision making than was possible before.108 Quantifying the exact value or benefit of closer integration is however a difficult task. Even in the relatively simple examples considered in the articles above, results are mostly obtained by simulation studies. One hypothesis which may be derived is that the benefit of integration increases with growing complexity of the SC setting. For example Chen (1998) observes in his model that cost reductions increase with a growing number of tiers present in the SC. Gavirneni et al. (1999) find substantial savings potentials when capacity is restricted at the supplier. Bourland et al. (1996) suggest that savings grow with increasing demand variability, whereas Lee et al. (2000) point out that a more complex (auto-correlated) demand process bears higher savings potentials from collaboration than i.i.d. random demand. On the other hand, growing complexity can as well lead to pooling of uncertainties, and hence a reduction of uncertainty. This can in turn reduce the value of information sharing as compared to scenarios without risk pooling. Cachon / Fisher (2000) e.g. observe average cost savings of 2.2% with inventory information. Although not mentioned by the authors, one potential reason for the relatively small gain can stem from the fact that their supplier serves N identical retailers, each facing random i.i.d. demand. Hence, the demand faced by the supplier is the aggregate over all retailers and therefore displays a lower variance than each retailer’s individual demand. Another interesting observation is that the value of collaboration can crucially depend on how the parties make use of shared information. As shown by Gavirneni (2002), a clever change of operating policies based to additional information can offer substantial benefits compared to simply incorporating the new data into the decision rules already in use. Now, how can these findings be transferred to the scenario considered here? The major difference to the SC settings studied in the articles above concerns the models used for decision making. Whereas rule-based inventory control policies are considered in the contributions above, we assume that mathematical programming models are utilized for generating plans. Without any coordination each domain creates a local forecast for its final output, which is updated regularly. The

107 108

C.f. Raghunathan (2001), p. 606. C.f. Gavirneni et al. (1999), p. 20.


41

inefficiencies resulting from isolated, domain-specific planning are caused by poor demand information, i.e. forecast quality, and the sub-optimization of the SC as a whole. With local forecasting and planning, fluctuations of the SC’s final demand propagate upstream from domain to domain with time delays and falsified by planning decisions at each domain (e.g. single period demands are aggregated to batches). Therefore, even with moderate fluctuations of final demand, demand variance often grows in upstream direction from domain to domain, as it is described by the bullwhip-effect.109 In result, moving upstream in the SC, demand becomes increasingly unpredictable. Since deterministic demand forecasts are used to drive planning by MPM, regular and substantial deviations from expected demand require frequent re-planning and lead to unexpected capacity shortages or unnecessary inventory stocks. To give an idea of the magnitude of additional costs due to low forecast accuracy, literature on rolling schedule performance can be consulted. For example, Venkataraman / Nathan (1999) study the impact of forecast errors on rolling master production scheduling. In computational tests based on data of a paint company they observe a difference in total cost of around 12% between a scenario where demand is on average overestimated by 20% and a scenario where it is underestimated by 20%.110 Even if all forecasts are perfectly accurate, local optimization within each planning domain results in sub-optimal plans for the SC as a whole. Naturally, planning domains at the SC’s most downstream tier have the privilege to plan first based on final demand forecasts. Second tier domains plan based on (forecasted) demand as requested by tier-one domains etc. From a total SC perspective this results in sub-optimization. Its degree is likely to grow with the number of tiers present in the SC, similar as in the model studied by Chen (1998). Also, results tend to increasingly deviate from the global optimum with a growing portion of total SC costs incurred at upstream domains. As we will see shortly, savings potentials of up to 35% were observed in simulation studies with three tier SCs.111 In summary, we can expect efficiency gains in line with the findings reported above. Namely that substantial cost reductions can be realized from the coordination of planning between domains, especially when demand variability is considerable, multiple tiers are present, and system constraints such as limited capacity are to be obeyed.

109 110

111

See e.g. Lee et al. (1997), pp. 93. C.f. Venkataraman / Nathan (1999), pp. 686. Unfortunately, the authors do not elaborate on cost differences to forecasts with small / none errors, i.e. high accuracy. Still, their results give an impression of the impact of accurate forecasting. C.f. Simpson / Erengüc (2001), p. 122.


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3.3

Coordination of Planning Processes Along the Supply Chain

After discussing benefits of information sharing and coordination between SC partners, we now turn our attention towards how to achieve coordination. Two distinct approaches are regarded for that purpose: coordination of SCs by contract terms on the one hand and coordination mechanisms for mathematical programming models on the other. Based on the modeling framework as introduced above, the latter approach is obviously of particular importance. Nonetheless, coordination by contracts provides interesting insights into the nature of coordination issues in SCs and should therefore not be omitted.112 3.3.1

Coordination by contracts

In free-market societies economic activity is based on voluntary exchanges between independent parties who enter contracts in order to mutually commit to specific transactions.113 In SCs with independent partners, supply contracts are the major means to regulate the terms of how partners do business together and are rewarded. Each party’s decisions in operating the SC are led by local incentives (i.e. profits or costs) and the uncertainty or risk faced with respect to demand, supply or internal processes. Both the incentives of individual partners as well as the risk they face is to some extent determined by supply contracts settled with SC partners. It is therefore natural to examine the effects of supply contracts on the behavior of individual parties and to adjust the terms of pricing and accountability such that individual entities are guided towards the globally desired outcome.114 This is studied in a large and growing number of publications on the coordination of SCs by contracts. Although to date a commonly accepted taxonomy of supply contracts and related research does not seem not to exist,115 some broad categories can be defined to classify the various contributions. One such differentiation concerns the purpose of the analysis put forward. Whereas some authors merely examine the implications of given contracts on individual parties (contract analysis), others go a

112

113 114 115

Another research area often regarded around the topic of SC coordination are multiagent systems. However, as agent systems are more a technology or means to implement decentralized control of a SC, they are not reviewed here. Interested readers are referred e.g. to Fox et al. (2000) or Grolik et al. (2001). C.f. Friedman (1982), pp. 13. C.f. Whang (1995), pp. 413. C.f. Tsay et al. (1999), p. 306, Zimmer (2001), p. 50.

3.3. Coordination of Planning Processes Along the Supply Chain

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step farther and try to devise contract terms that yield optimal performance for the SC as a whole (contract design).116 Another classification distinguishes whether only financial incentives are regarded, risk and risk sharing issues prevail, or both aspects are dealt with in conjunction.117 Finally, an important distinction should be made between contributions where full information is available to the party that sets the contract terms, and others that (more realistically) assume information asymmetry.118 A comprehensive review of this large body of literature shall not be given here.119 However, some well-known examples are introduced in the following in order to give an overview of the type of analysis and results that are brought about. 3.3.1.1

Coordination of joint lot-sizing

Monahan (1984) is among the first to elaborate on how individual cost incentives yield sub-optimal results for the SC as a whole. He considers a buyer that faces stationary, deterministic demand for a single product which he purchases from a supplier at given price and fixed ordering costs. The supplier produces lot-for-lot whenever an order arrives and is himself confronted with fixed setup costs. Since the product is stockable at the buyer (incurring holding costs), the buyer’s decision situation corresponds to the traditional economic lot-size problem (EOQ). However, the buyer’s locally optimal lot-size and replenishment interval is not optimal for the total SC, because, in determining the lot-size, he neglects the supplier’s setup cost. The resulting lot-size is hence smaller than the jointly optimal quantity. To counteract, Monahan (1984) proposes that the supplier offers a quantity discount to the buyer for orders of at least the jointly optimal lot-size.120 The total rebate (price discount × lot-size) is chosen such that the buyer is compensated for the extra cost compared to his locally optimal policy. In that way the supplier can induce the buyer to order in jointly optimal quantities. Monahan’s article sparked a series of follow-up publications that expand the basic framework. For example, Lee / Rosenblatt (1986) drop the lot-for-lot production assumption for the supplier, obtaining a significantly more complex problem.121 Weng (1995) considers the case where final demand is price-sensitive, and Chen et al. (2001) a scenario with multiple buyers and price-sensitive demand.122 For all these problems discount schemes can be determined from the supplier’s perspective that coordinate the SC, i.e. induce the buyer(s) to employ jointly optimal order policies.

116 117 118 119

120 121 122

C.f. Anupindi / Bassok (1999), pp. 201. C.f. Zimmer (2001), p. 25. C.f. Corbett (2001), p. 487. Interested readers are referred to Tsay et al. (1999), pp. 301, Zimmer (2001), pp. 50, Cachon (2003), pp. 229. C.f. Monahan (1984), p. 723. C.f. Lee / Rosenblatt (1986), pp. 1178. C.f. Weng (1995), p. 1512, Chen et al. (2001), pp. 693.


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All the above contributions assume that full information is available to the supplier when defining the discount scheme. It is therefore interesting to observe how the situation changes when information is asymmetric, i.e. certain parameters of the problem setting are unknown to the supplier. A major example for this situation is presented by Corbett / de Groote (2000). They essentially deal with the problem of Monahan (1984), however assume that the buyer’s fixed order cost is negligible and, more importantly, his holding cost rate is unknown to the supplier. Without knowledge of holding cost it is not possible for the supplier to determine the jointly optimal lot-size and discount to offer to the buyer. To resolve this, the supplier announces a “menu of contracts” with several discount rates and minimum order quantities (lot-sizes). The menu is derived from estimating an interval [ h, h] of the buyer’s holding cost rate. The buyer then chooses his preferred discount scheme, thereby in effect disclosing his holding cost rate (so called revelation principle).123 However, although the resulting discount scheme improves total costs, optimality for the entire SC is no longer guaranteed. As stated elsewhere by Corbett (2001), incentive and information issues together “generally lead to inefficient outcomes, even under an optimal menu of contracts”.124 Sucky (2006) extends the work of Corbett / de Groote by including a fixed buyer order cost, which, too, is unknown to the supplier. He, however, also uses a very simplistic approach, assuming that the supplier knows that the buyer is one of two types (i.e. either has holding cost h1 and order cost x1 or h2 and x2).125 He shows that in this setting the supplier can also use a menu or contracts to induce the buyer to order the jointly optimal quantity. An overview of publications on lotsizing problems in SCs is given by Sarmah et al. (2006). 3.3.1.2

Coordinating the “news vendor”

The basic model that deals with final demand uncertainty, and hence risk sharing between SC partners, is the news vendor problem. Here the buyer faces stochastic demand for a single product which he has to order from the supplier prior to realization of actual demand. Unmet final demand incurs loss of revenue and (potentially) lost sales costs; excess supply can be sold by the buyer at a salvage rate below the actual market price.126 The supplier in turn faces linear production costs and likes to sell as large a quantity as possible at a price above unit cost. How much the retailer commits to buy depends on the contract terms, and hence on how the risk of stock-outs and obsolescence is shared between him and the supplier. A simple wholesale price contract where the supplier charges a fixed unit price fails to coordinate the SC.127 However, various contract types can be devel-

123 124 125 126 127

C.f. Corbett / de Groote (2000), p. 447. Corbett (2001), p. 488. C.f. Sucky (2006), p. 526. See e.g. Silver et al. (1998), pp. 385. C.f. Lariviere / Porteus (2001), p. 293.


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oped which induce the buyer to adopt the globally optimal order quantity. For example, Lariviere (1999) discusses how coordination can be achieved by franchising, quantity forcing, a buy-back option offered by the supplier, and a quantity flexibility scheme.128 Cui et al. (2007) introduce fairness considerations in the newsvendor problem and show that a wholesale price contract achieves coordination when the channel members care about fairness.129 An overview of contractual settings for the news vendor problem and various extensions, including a case with asymmetric information regarding the final demand distribution, is presented by Cachon (2003).130 3.3.1.3

Coordination of multi-level inventory systems

A more complex SC setting is studied by Lee / Whang (1999). It resembles a serial multi-echelon inventory system with stochastic final demand. Each echelon orders material from its upstream neighbor and bears holding costs for local inventory. Orders are met after a constant lead time, and backordered as far as existing inventory is insufficient to meet the full amount. Achieving coordination in such a system is again a matter of risk sharing. Since only the most downstream echelon pays backorder penalties to external customers, upstream echelons have no incentive to carry costly inventory. Hence, without any coordinating arrangements it is up to the downstream party to hedge vs. uncertainty of demand and supply, which results in sub-optimal performance. Therefore, Lee / Whang (1999) show how the optimal control policy as developed by Clark / Scarf (1960) from a central planner’s perspective131 can be implemented based upon a sophisticated incentive scheme. In particular, they propose a combination of transfer pricing, consignment, backorder penalty, and shortage reimbursement for measuring the performance of individual echelons.132 3.3.1.4

Implications for this work

In conclusion, SC coordination by contracts usually deals with relatively simple SC structures, e.g. an isolated perspective of single products is taken, assuming constant or stationary stochastic demand. Based on such models, SCs are operated according to inventory-control policies as e.g. described by the EOQ-solution or order-up-to policies in case of stochastic demand. Since supply contracts affect the choice of (locally) optimal control parameters, contract terms can be used to entice individual parties to act in a globally desired way. However, defining coordinating

128 129 130 131 132

C.f. Lariviere (1999), pp. 246. C.f. Cui et al. (2007), pp. 1302. See Cachon (2003), pp. 229. I.e. echelon stock re-order point policies (c.f. Clark / Scarf (1960), pp. 476). C.f. Lee / Whang (1999), p. 636. A similar solution to the same problem is presented by Chen (1999), pp. 1079, except that transfer payments are gathered and granted by a central coordinator, e.g. headquarters of a decentralized firm.


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contract terms is a complex issue even in these relatively simple problem settings. Moreover, it requires knowledge of all relevant cost and demand parameters. Without full information the situation becomes less tractable and perfect coordination (i.e. achieving the optimal solution for the SC as a whole) is no longer achieved. What are the implications for a scenario as condisered here with multiple products competing for common resources such as capacity or raw material supplies, and where planning is based on mathematical programming models and demand forecasts by period? In such a situation, plans are re-generated periodically and optimal results are not stationary. Of course, terms of supply contracts can be incorporated in mathematical programming models too.133 However, it is hardly possible to achieve SC optimality by setting contract parameters at a single point in time. Much rather, it appears reasonable to change the order of events such that plans are coordinated first based on a given coordination mechanism. Supply contracts are then adapted in a second step in order to ensure that the parties get incentives to adhere to the defined planning results. Achieving coordination hence requires other mechanisms to integrate planning between independent domains. Such mechanisms are discussed in the following section. 3.3.2

Coordination mechanisms for mathematical programming models

Two coordination mechanisms as proposed in the literature for the coordination of MPM-based planning are introduced in the following: first the simple, sequential Upstream Planning scheme (including possible extensions to it), and second the Lagrangean relaxation approach. A structured, more detailed classification of the publications referenced below is presented in Stadtler (2007).134 3.3.2.1

Upstream Planning and extensions

Upstream Planning represents the simplest mechanism which can be utilized for the coordination of planning across several domains. It is for example described by Bhatnagar et al. (1993) and also referred to as “top-down planning” by some authors.135 The idea is to perform planning level-by-level or tier-by-tier and to pass resulting order requirements of downstream domains to their suppliers. This is visualized in Fig. 10 for two planning domains. The downstream domain plans first

133

134

135

See e.g. Tempelmeier (2003), pp. 366, for a model to plan purchasing quantities based on several discount rates offered by a supplier. The publications are classified along the SC structure studied, the decision situation captured and characteristics of the coordination mechanisms used (c.f. Stadtler (2007), p. 8.) C.f. Bhatnagar et al. (1993), p. 147, Zimmer (2001), pp. 146.


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based on a forecast of its external demand. Order requirements are derived from this plan and communicated to the supplier. Then the supplier domain plans based on the order quantities. If this domain in turn has suppliers, the scheme can continue analogously. Domain 2

Domain 1

Supply requirement s

Ext ernal dem and

3. Generat e opt imal plan

1. Generat e opt imal plan

4. Derive order quant it ies

2. Derive order quant it ies

Fig. 10. Upstream Planning scheme

In terms of the planning model of section 3.1 the downstream domain generates its plan by solving Model 1 enhanced by constraints (11) so that order quantities directly result from variables xsj,t. Resulting values are transmitted to domain 2 which too plans by utilizing Model 1, this time enhanced by constraints (14) and (15) so that received order quantities (XOj,t) are input to the model. Although not shown in the figure, several, independent domains (i.e. not linked by supply relationships) can be present at any tier just as well. The only prerequisite is that a tier-by-tier order of domains can be established. This is possible, as long as no cyclic supply relationships exist between domains, i.e. no domain is supplier and customer of another one at the same time, even if this happens indirectly via other, intermediary domains. Upstream Planning is superior to completely isolated planning within each domain, because order requirements are passed on from customers to suppliers and form the basis of planning at suppliers. Hence, the plans of individual domains become consistent one with another, and all ground on the demand forecast of the most downstream party. In consequence, inefficiencies from unsynchronized operations are eliminated, namely high inventory buffers at the interfaces between domains and frequent re-planning due to deviations of actual orders from local demand forecasts. Also, the scheme is straightforward to implement and requires little effort to achieve coordination. It is therefore, why Upstream Planning is the predominant form of CP found todate in practice. Suppliers get access to customers final demand data and planned order quantities and base their local planning on this information instead of using local demand forecasts. However, as Bhatnagar et al. note, Upstream Planning’s drawback is that “it ignores the interactions between various plants and will yield sub-optimal produc-

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tion plans”.136 This is because each domain generates locally optimal plans (based on received order quantities and/or forecasted external demand) without taking account of the consequences of local decisions on upstream partners. Hence, from a total SC perspective, the scheme produces inferior results compared to centralized planning with a simultaneous optimization of the SC as a whole. In order to quantify the level of sub-optimality, Simpson / Erengüc (2001) perform a computational evaluation of an example SC setting. They consider three tiers with several retailers (tier 1) ordering multiple products at a single distribution center (tier 2), which in turn replenishes the products from several manufacturers (tier 3). Fixed order or setup costs are balanced with end-of-period inventory holding costs at all tiers. Simpson / Erengüc model the planning situation as a multi-level lot-sizing problem and compare tier-by-tier Upstream Planning solutions to those of centralized planning. 137 On average, they observe a cost gap between centralized and Upstream Planning of 14.1%. A key insight of the authors is that the gap grows with an increasing portion of total cost incurred at upstream domains. This is, because the effect of unfavorable order requirements on total SC costs gets larger. In the computational study, the average gap is merely 1.8% for test problems where the manufacturers bear 29% of total cost, but 9.0% when they bear 41% and 31.5% when they bear 51% of total cost.138 The study by Simpson / Erengüc makes apparent that Upstream Planning can produce sufficiently good solutions in some SC settings (namely when the most of total costs is incurred at the downstream tier). However, substantial improvements can be reached in many cases, when more sophisticated coordination schemes are used. As the Upstream Planning mechanism is easy to implement, one way to obtain better performance is by developing extensions to its basic form, intended to produce better solutions while keeping the basic tier-by-tier planning process. One such approach is developed by Zimmer (2001), who enhances Upstream Planning by anticipation.139 The idea is to add major constraints from the supplier domain (in a simplified form) to a downstream domain’s planning model, and thereby obtain improved overall planning results. Zimmer studies a scenario with two SC partners, a manufacturer and a supplier. She assumes contract terms which allow the supplier to deviate from order requirements, however at penalty costs for early and late deliveries (the total order volume must remain unchanged). Both parties use MPM for planning of their operations. The supplier’s objective is to minimize costs of operations as well as contractual penalties. When the supplier’s deliveries deviate from orders, the manufacturer needs to re-plan based on given supply availability.

136 137 138 139

Bhatnagar et al. (1993), p. 147. See Simpson / Erengüc (2001), pp. 120, for details. C.f. Simpson / Erengüc (2001), pp. 122. The concept of anticipation has already been introduced in section 2.3.2 within the overview of hierarchical planning (s. pp. 15).


49

Zimmer considers two types of anticipation: non-reactive and reactive. In the first case, the major restrictions of the supplier domain are added to the manufacturer’s planning model so that planning results become jointly feasible. Specifically, she adds capacity constraints for order quantities by period and an upper limit on the capacity extension which the supplier may be willing to accept for ensuring timely deliveries.140 For evaluating the performance gain, a computational study is carried out similar to Simpson / Erengüc: solutions of mere Upstream Planning, Upstream Planning with anticipation, and centralized planning are compared. In result, an average cost reduction of about 20% can be realized by nonreactive anticipation. However, as mere Upstream Planning results are on average 190% off from centralized planning solutions (due to high costs of capacity extensions), the gap remains substantial.141 This is not surprising, as anticipation through additional constraints only aims at preserving plan feasibility at the supplier domain, but does not guide decisions by cost effects resulting for the upstream party. Also, only estimates of the supplier’s capacity and other parameters are available to the manufacturer. Due to these shortcomings Zimmer develops a second, more complex scheme referred to as reactive anticipation. Generally, in reactive anticipation the (likely) reaction of the base-level on top-level decisions is explicitly considered, so that cost considerations can be regarded.142 The idea is to establish an iterative procedure where the base-level reaction is simulated and fed back to the top-level model. This is re-run with the additional information to produce a revised plan, and so forth until satisfactory overall results are observed. Zimmer proposes to use such a scheme to adapt the contractual penalty cost rates for early and late deliveries in a way that induces the supplier to act in the total SC’s interest. Initially, the manufacturer solves a centralized planning model of the entire SC. Order requirements corresponding to the resulting plan and penalty rates of zero are input to the anticipated base-level model. If the anticipated supplier’s behavior differs from the centralized planning results (which is usually the case), the penalty rates are increased step-wise and the anticipated supplier model is re-solved. In this way Zimmer intends to find penalty rates which induce the supplier to adopt to the centralized planning solution.143 Computational results show that this scheme comes close to centralized planning solutions with an average gap of 8%.144 However, this comes at the expense of high information needs by the manufacturer and largely increased complexity. The entire supplier planning model must be available to the manufacturer. Also, although not commented upon by Zimmer, a significant number of iterations can

140

141 142 143 144

See Zimmer (2001), pp. 156, for details. This anticipation concept has in fact been realized in a SC project in the automotive industry (c.f. Hirzel et al. (2002), pp. 64). C.f. Zimmer (2001), pp. 197. C.f. Schneeweiss (1999), pp. 43. C.f. Zimmer (2001), pp. 181. C.f. Zimmer (2001), p. 199.


50

be expected necessary for finding the “optimal” penalty cost rates. Finally, it is questionable whether contract terms can be set by the manufacturer alone, as they usually are a result of negotiations, and whether they can be re-adjusted dynamically in every planning cycle. Nevertheless, this work is a valuable contribution as it outlines how mere Upstream Planning can be improved by extending planning considerations beyond local circumstances. 3.3.2.2

Lagrangean relaxation approach

For discussing the Lagrangean relaxation approach it is best to start with the perspective of centralized planning, i.e. to consider a single MPM which covers several, say N, planning domains. Such a model consists of an objective function, N sets of constraints that pertain to individual domains, and a set of constraints linking individual domains by inter-domain flow balance equations. Using the modeling framework presented above, the centralized model comprises several instances of Model 1 (each for a single domain) and inter-domain links expressed by constraints (11) and (14) linking consumption of intermediary items to their supply. The model’s matrix of coefficients is depicted in Fig. 11 (columns correspond to decision variables and rows to the objective function and constraints). Formally, it can be written as follows: min s.t.

CX A1 X ≤ B1

(16)

A2 X = B 2

where the first set of constraints corresponds to domain-specific restrictions and the second to inter-domain links. Now, it has a long tradition in Operations Research that large-scale MPM of a structure as presented in Fig. 11 are decomposed to more tractable subproblems.145 A solution to the original model is then obtained by a mechanism which coordinates the solution procedures of sub-models. The standard way to decompose the original model, called Lagrangean relaxation, is by “dualizing” the constraints linking individual domains; that is by removing linking constraints from the model’s constraint set and adding them to the objective function. Mathematically, the term λ ( A2 X − B2 ) is added to the original objective function, where λ is a vector of Lagrange multipliers λi. Without domain linking constraints the model separates into N domain-specific sub-problems which can be solved individually. Since the individual optimal solutions depend on the values of λi, which represent a penalty in each submodel’s objective function, these parameters can be used to coordinate sub-model solutions.

145

See e.g. the decomposition schemes by Dantzig / Wolfe (1960) and Benders (1962). The original goal of decomposition schemes was to divide a large MPM into smaller ones in order to reduce the computational complexity of its solution.


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This is usually accomplished by an iterative procedure where, for given solutions, the violation of relaxed constraints is analyzed and the parameter values λi are adjusted repeatedly.146 However, a difficulty often arises with such iterative methods when binary variables are included in domain-specific sub-models. Then, globally feasible solutions can hardly be obtained due to the models’ integrality gaps.147 In order to still find feasible solutions, heuristic methods can be used to rearrange obtained solutions such that feasibility is preserved. decisions variables constraints

Obj fct. Dom. 1 Dom. 2

Dom. N Domain links

Fig. 11. Structure of a centralized planning model (source: Holmberg (1995), p. 67)

Within the context of operations planning in SCs, Barbarosoglu / Özgür (1999), Ertogral / Wu (2000), Karabuk / Wu (2002) and Jung et al. (2005) develop Lagrangean relaxation based procedures for coordinating planning across individual domains. Barbarosoglu / Özgür study a SC with several customers who order multiple products from several depots, which in turn order at a single plant. Fixed order / setup and inventory holding costs are incurred at each facility, and production capacity is restricted at the plant. The authors first develop a single MPM for centralized planning. Then, they introduce Lagrangean relaxation with respect to the balance constraints which link production levels at the plant with shipments to the depots. In result, the model separates into sub-models for production and distribution. In order to coordinate the sub-models, sub-gradient optimization is proposed. I.e., when the sub-models are solved with given Lagrangean multipliers, the inconsistency of relaxed constraints is checked by a central agent. When the total in146

147

A heuristic search by sub-gradient optimization is mostly proposed for this process step (c.f. Shapiro (1979), p. 124, Fisher (1985), pp. 12). C.f. Fisher (1981), pp. 14.

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consistency for a product-period combination is measured by γi,t, the corresponding multiplier is updated according to λi k +1 = λi k + α k γ i ,kt

(17)

where k is the iteration counter and α a normalizing factor which is dynamically adjusted through the course of the procedure.148 A difficulty is however caused by the binary variables present in both submodels. Since altering binary decisions strongly affect other variables (e.g. production levels), it is questionable whether a smooth convergence of the submodels can be expected. Unfortunately, this feature is not analyzed the Barbarosoglu / Özgür. However, they do report that consistent solutions can rarely be obtained by the scheme.149 In order to still achieve consistency, they propose a simple, hierarchical heuristic which is applied once the sub-gradient optimization has terminated: the final distribution plan is fixed and a compatible production plan is generated with the production sub-model.150 Jung et al. (2005) study a SC with a production and a distribution tier. They use separate planning models for each tier, which are coordinated by Lagrange-type penalties in the objective function for deviations between requested and proposed order quantities.151 As their planning models are linear, i.e. do not contain binary variables, reasonably good results are achieved within a few iterations – at least with a numerical example presented by the authors. Ertogral / Wu (2000) consider production planning across several plants where each plant has limited capacity and tries to minimize setup and inventory holding costs. The decision situation is first modeled from a total SC perspective by the MLCLSP as given by Model 1 above. Then, Lagrangean relaxation is applied to flow balance equations to decompose the MPM to facility sub-models just as in Barbarosoglu / Özgür (1999). To coordinate the sub-models, Ertogral / Wu first implement sub-gradient optimization. However, they report that computational tests reveal oscillations of sub-models between a few solutions depending on the values of Lagrange multipliers.152 Therefore, they expand the coordination mechanism in a way that ensures convergence of sub-model solutions. To do so, they use target values for interdomain flow variables in addition to the Lagrange multipliers. The multipliers are then used as penalty cost rates for deviations of the target values. Furthermore, multipliers and target values are updated by a central coordinator based on deviations from each sub-model’s minimum cost solution obtained in the first iteration. Thereby, the scheme does no longer aim on minimizing total SC costs, but to find

148 149 150

151 152

See Barbarosoglu / Özgür (1999), p. 474, for details. Barbarosoglu / Özgür (1999), p. 474. So, in a sense the scheme is similar to Upstream Planning. If the distribution plan turns out not to be feasible at the production stage, a simple, rule-based algorithm is used to modify distribution decisions (c.f. Barbarosoglu / Özgür (1999), p. 476). Jung et al. (2005), pp. 102. C.f. Ertogral / Wu (2000), p. 936.


53

consistent and “fair” overall solutions. That is, solutions with equal deviations from minimum cost results across all sub-models.153 In a computational study the authors demonstrate that solutions converge, i.e. consistent results can be obtained. The average deviation of costs vs. optimal results of centralized planning is around 10%. However, Ertogral / Wu emphasize the fairness issue in discussing the results. Here, the solutions obtained by their scheme clearly outperform centralized planning. Finally, Karabuk / Wu (2002) use a Lagrangian technique to coordinate a production and distribution domain, which use stochastic, linear programs for operations planning. As the assumed models are linear, the authors can show that their scheme converges to a single solution.154 Summarizing the above, Lagrangean decomposition represents a second mechanism for the coordination of planning across individual domains. It is in fact an elegant approach, since long known techniques of mathematical programming can be directly applied to the decentralized problem environment considered here. However, as the examples of Barbarosoglu / Özgür and Ertogral / Wu indicate, it is not realizable without tackling some difficulties. For one, the common coordination method of sub-gradient optimization is troublesome when binary or integer variables are present in all or most of the submodels. Consistency between sub-models might not be achieved due to the duality gaps of the mixed-integer models. Moreover, oscillations of sub-models can occur that can entirely prevent convergence towards a stable solution. Even when these problems are resolved as in the above contributions, a critical prerequisite remains, which is the presence of a central coordinator required for updating multipliers and other directives. The standard metaphor for the decomposition approach described in literature is one of a decentralized firm where divisions take most of decisions on their own, but some control is exerted by a headquarters.155 However, the SC setting as considered here naturally lacks a central coordinator. Such a coordinating agent must therefore be newly established which in turn might not be appreciated by all partners. 3.3.2.3

Summarizing overview

Overall, we have seen three coordination schemes in the previous paragraphs. In order to give a summarizing snapshot of the different approaches, an overview and comparison of some properties concludes this chapter. Centralized planning by a single model for the whole SC is added to the overview for comparison. The coordination mechanisms are: • Upstream Planning, i.e. tier-by-tier generation of plans in upstream direction with communication of order quantities from customers to suppliers,

153 154 155

See Ertogral / Wu (2000), pp. 936, for details. C.f. Karabuk / Wu (2002), pp. 751. See e.g. Holmberg (1995), pp. 61.

54


• Upstream Planning with anticipation, i.e. Upstream Planning where intradomain planning models are enhanced by anticipated constraints or models of supplier domains, • Lagrangean relaxation, i.e. iterative generation of local plans (based on a common forecast of final demand), controlled by directives computed by a central coordinator between iterations, and finally • Centralized Planning, i.e. a single planning model, and hence a single plan for the entire SC generated by a central coordinator. A number of characteristics can be relevant for comparing the mechanisms, such as the quality of solutions or the computational effort to obtain them, just to mention two. However, two properties shall be regarded here in more detail, as they are of particular importance for the acceptance and applicability of the schemes to SC partnerships. These properties are: 1) the required degree of integration and 2) the schemes’ inherent level of hierarchy. Integration here refers to the type and amount of information that has to be exchanged between the partners (or between the partners and a central coordinator). It is a crucial measure, because, despite all SC integration efforts, most companies are reluctant to open sensitive information to outsiders. The level of hierarchy relates to the extent to which there are differing levels of decision authority assumed in a scheme. This, too, is a crucial question, as all parties must be willing to cooperate. However, if they are largely exposed to decisions made by others, the acceptance of a coordination scheme is questionable. The degree of integration and hierarchy can be combined to a conceptual matrix as shown in Fig. 12. When we try to place the coordination schemes into the matrix, a picture as indicated in the figure occurs. An extreme position is taken by centralized planning, as it requires both, a high degree of integration and hierarchy. The owner of the planning process (may it be one of the domains or a third party) must have all necessary information available, which requires strong informational bonds to all parties. Planning results are imposed on all domains, hence there is a high degree of hierarchy. Due to these properties centralized planning is often not applicable in settings with independent domains, as already discussed in section 2.3.2. In contrast, Upstream Planning requires a relatively low integration of planning domains. The only data exchange corresponds to order quantities passed from customers to suppliers. The scheme assumes however hierarchical relationships between planning domains, in the sense that upstream parties plan first and downstream suppliers take order quantities as given data. Hence, here too we find a relatively high degree of hierarchy. This remains unchanged in Upstream Planning with anticipation. But, as anticipation is only possible by gaining knowledge of supplier characteristics, the level of integration is higher, although clearly not as high as in centralized planning. Also, the exact type and amount of information required depends on how anticipation is realized.


high

55

Centralized Planning

Hierarchy

Upstream Planning

Upstr. Pl. + Anticipation Lagrange Decomposition

low low

Integration

high

Fig. 12. Integration – hierarchy matrix of coordination schemes

Finally, the Lagrangean relaxation approach entails a medium degree of integration, similar to Upstream Planning with anticipation. Here, consistent demand forecasts must be available to all domains. Order and shipment quantities are communicated to the central coordinator, and, in return, coordinating directives from there to the planning domains. Obviously, some level of hierarchy is present in this coordination scheme, too. However, as domains plan individually and the central coordinator’s role is restricted on checking the consistency of individual results and adjusting some coordinating parameters, the scheme can be regarded less hierarchical than centralized and Upstream Planning. In conclusion, one can observe that information exchange is necessary to obtain coordinated results, i.e. collaborative planning is only realizable when the parties accept some degree of integration. However, the coordination schemes presented above all involve a considerable degree of hierarchy as well. This fact can hamper their acceptance, as one may argue that truly non-hierarchical coordination remains a myth here. It is for that, and also other reasons such as quality of solutions and general applicability, why an alternate, innovative scheme for collaborative planning is developed in the next chapter. Recommended readings • Rohde J. / Wagner M. (2005): “Master Planning”, in: Stadtler, H. / Kilger, C. (Eds.): Supply Chain Management and Advanced Planning – Concepts, Models, Software and Case Studies, 3rd ed., Berlin et al. 2005, 159-177. • Gavirneni, S / Kapuscinski, R. / Tayur, S. (1999): “Value of information in capacitated supply chains”, in: Mgmt. Science, Vol. 45(1), 16-24.

56

•

• • •

3. Modeling Framework and Relevant Literature Cachon, G.P. (2003): “Supply chain coordination with contracts”, in: Graves, S.C. / de Kok, A.G. (Eds.): Supply Chain Management – Design, Coordination and Contracts – Handbooks in Operations Research and Management Science, Vol. 11, Amsterdam et al. 2003, 229-339. Sarmah, S.P. / Acharya, D. / Goyal, S.K. (2006): “Buyer-vendor coordination models in supply chain management”, in: European Journal of Operational Research, Vol. 175, 1-15. Barbarosoglu, G. / Özgür, D. (1999): “Hierarchical design of an integrated production and 2-echolon distribution system” in: European Journal of Operational Research, Vol. 118, 464-484. Stadtler, H. (2007): “A framework for collaborative planning and state-of-theart”, in: OR Spectrum, online edition.

4 Negotiation-Based Collaborative Planning between Two Partners Content In this chapter we develop a collaborative planning scheme for a single buyersupplier pair. The following section describes the supply chain scenario and presents an overview of the scheme. The distinct planning steps carried out repeatedly by the collaboration partners are presented in full detail in section 4.2. Thereafter, section 4.3 deals with the resulting total process flow and its control. Section 4.4 concludes the chapter with a brief summary and some final comments. Key points • We formalize a negotiation-like, iterative process between the supplier and buyer. Order proposals (generated by the buyer) and supply proposals (generated by the supplier) are passed between the parties in an iterative manner. • A proposal received from the partner is analyzed for its consequences on local planning and a counter-proposal is generated by introducing partial modifications. Resulting is a process which subsequently improves supply chain wide costs without centralized decision making and with limited exchange of information. • Mathematical programming models as introduced in section 3.1 are used throughout all stages of the process.

4.1

Assumptions and Overview

Throughout this chapter we consider only two planning domains, a buyer and a supplier, which are connected by supplies of (physical or intangible) products. Internally, each planning domain may cover a multitude of (inter-connected) operations stages. As shown in Fig. 13, the two parties coordinate their operations by collaborative planning. All remaining customers and suppliers are assumed to be out of influence. Hence, demand (forecasts) and potentially supply capabilities pertaining to other entities represent given data. Based on our discussion in section 3.1 plans are generated within each domain by the use of MPM such as Model 1. Supply or order links to the collaboration partner can be explicitly included in the planning model as presented in section 3.1.3. We consider one-time planning, i.e. a situation where the partners coordinate their plans over the entire planning interval for a single time. In terms of the contractual setting, the supplier is assumed to charge a simple fixed unit price. Thus, the payment received by the supplier is fixed for a given total purchase volume, and therefore not explicitly regarded in the following.


58

4. Negotiation-Based Collaborative Planning between Two Partners

As we have seen in the literature review of section 3.3.2, mechanisms proposed in the literature for coordinating planning by mathematical programming models assume hierarchical relationships between the parties and require a varying degree of integration of the individual planning domains. As already argued above, demanding a hierarchical structure and strong bonds between the parties may however hinder a scheme’s acceptance by independent decisions makers across a SC. Supplier

Buyer Collab. Planning

Supply

External supply Domain 2

External demand Domain 1

Collaboration

Fig. 13. Two party collaborative planning

The purpose of this chapter is therefore to develop a novel approach for collaborative planning, which should ideally exhibit the following properties: • • • •

non-hierarchical relationships, exchange of uncritical and only as few as possible data, consistent, implementable plans in each iteration, and demonstrably good solutions with a small number of iterations.

As independent decision makers will usually not be satisfied with a subordinate role of implementing pre-set decisions and reporting some feedback on those decisions at the maximum, the scheme presented here tries to give all partners similar decision rights and authority. Also, it should be clear that the willingness to participate in collaborative planning depends on the type and amount of internal data opened to SC partners. The nature of exchanged information should therefore be as uncritical as possible. Although sensitivity of data is always a matter of subjective judgment,, some type of information (e.g. order requirements) can be generally regarded less sensitive than others (e.g. internal cost rates).156 Plan consistency is a more technical, but still important requirement. It ensures that implementable plans are in place, even if the coordination scheme is aborted at some early stage. This way a compatible overall plan for all partners is obtained in any case. The fourth characteristic finally considers the computational effort re156

Kersten (2002), p. 16.

4.1. Assumptions and Overview

59

quired to obtain a satisfactory overall solution. As we face complex decision situations at each domain and hence deal with large, computationally challenging planning models, the scheme should not entail hundreds of iterations prior to realizing an improvement. Instead the total outcome should be effectively improved within a reasonable time frame. The approach developed in the following rests on the idea of a “negotiation among equals”. It assumes an equal, active role for all partners. As a metaphor we can think of supply chains planners holding a meeting to manually coordinate their respective plans. Each planner will analyze the consequences of partner plans and actively propose modifications that improve his situation. Eventually, the planners will commit to compromise solutions. The same logic applies to the scheme presented below. In a first step, any given partner order / supply proposal is analyzed. Second, as the partner requirements usually cause a deviation from the locally optimal plan, targeted modifications to the order / supply pattern are generated and proposed to the partner. The partner then carries out the same process of analyzing the modified order / supply pattern and introducing new modifications to it. Modifications can however only be made to a limited extent. Otherwise, the parties would re-generate their original order / supply pattern as their preferred situation. Therefore, the idea is to only allow for the most effective modifications. Those modifications create the largest local cost improvement per unit change, thereby also offering the greatest chance for a total supply chain cost improvement. The negotiation process is visualized by a demonstrative example in Table 6. The buyer purchases three items. The planning horizon covers 12 periods, of which only the first four periods of the order / supply pattern are shown in Table 6. The quantities represent cumulated orders / supplies from period 1 through t. As cumulated figures immediately indicate an excess or short supply up to a given period, they are commonly used for describing order / supply patterns in the following. The top contains the initial order pattern requested by the buyer based on his locally optimal plan. If the supplier fully covers the order requirements, he faces costs of 129,574 monetary units (MU). Total supply chain costs sum up to 228,241 MU. Based on this initial Upstream Planning solution, the supplier proposes a modified supply pattern as shown in the second section of Table 6.157 We see that most changes refer to item 1, item 2 supplies are modified in periods 1 and 4, and item 3 supplies only in period 2. The modifications result in a cost decrease for the supplier of 9,452 MU and in a cost increase for the buyer of 4,060 MU. Hence, the new proposal creates net savings of 5,392 MU compared to the initial situation. The buyer proposes additional modifications (section 3) by partly returning to his initial orders (e.g. item 1, period 3; item 2, period 1) and partly introducing new changes (e.g. item 2, period 4). The modifications decrease local cost by 2,048 MU and increase cost at the supplier by 337 MU. In total, additional net savings of 1,811 MU can be achieved. According to the iterative nature of the

157

Excess supplies (vs. the initial orders) are printed bold, short supplies italic and bold.


60

process the supplier suggests further modifications, thereby once more generating significant additional savings. The process may continue as long as additional savings occur. Table 6. Negotiation process example

Data Ex- Period change Item. B→S

S→B

B→S

1

2

1

168

230

2 3

77 247 122 239 247

239 347 363 239 299

95 77 247

363 239 347

363

426

239 548

404 650

95 77 347

397

397

397

404 442

404 442

404 869

1 2 3 1 2 3

S→B

1 2 3

3

4

Cost B

Cost S

Cost Total

363

397

98,667

129,574

228,241

239 548 397 239 548

375 650 397

102,727

120,122

222,849

100,679

120,459

221,038

105,451

106,228

211,679

431 650

In order to realize the above process, the collaboration partners need to exchange the respective order / supply patterns as well as local savings incurred by the proposed modifications. With this knowledge, the planning partner can evaluate the total effect (i.e. partner + local) of the modifications. The example demonstrates that, with the proposed scheme, both partners have the same decision authority, i.e. the scheme represents a heterarchical coordination process. Also, a consistent overall plan is generated in each iteration. The example gives a first indication that significant cost improvements can be obtained with a few iterations. Of course this property will be analyzed in greater detail later.158 Besides the order / supply patterns exchanged data only comprises local savings, an aggregate measure, which we assume a rather uncritical information. With this overview in mind, we can now consider the outlined scheme in more detail.

158

Through an extensive computational evaluation presented in chapter 7.

4.2. Iterative Planning Steps

4.2

61

Iterative Planning Steps

As we have seen above each planning domain repeatedly evaluates received order/ supply proposals and generates compromises as counter proposals in reply. These basic planning activities hence represent the distinct process steps carried out in each iteration and are described in detail in the following. The way in which the compromise generation is accomplished however requires an intermediary step, which determines a party’s most preferred outcome, that can be derived from the partner’s current proposal. This process step is therefore described before the actual compromise generation. Moreover, a compromise order/ supply pattern is not guaranteed to differ from patterns proposed in former iterations. Therefore a method is introduced which compares a compromise pattern to former proposals and generates additional compromises, if the order/ supply pattern is equivalent to a previously proposed pattern. Also, in order to avoid infinite cycling, a stopping rule can terminate the generation of additional compromises.159 Although the tasks are equivalent for the buyer and supplier, the order/ supply pattern plays a different role for each party. Thus, distinct models corresponding to the buyer and supplier are presented for each process step. A flow chart of the iterative planning steps is given in Fig. 14. It shows the sequence of activities carried out by each partner in one iteration as just described. An iteration hence is defined to embrace the subsequent evaluation of the partner proposal and generation of a counter-proposal by both buyer and supplier.160 Each of the following sections is dedicated to one of the iterative planning steps as also implied in Fig. 14. 4.2.1 Evaluate partner proposal

4.2.2 Determine preferred outcome

4.2.3 Generate compromise

4.2.4 1. New compr. ? 2. Stop anyway ? no Generate additional compromise

Fig. 14. Iterative planning steps - flow chart

159 160

Details follow below in section 4.2.4. A thorough description is laid out below in section 4.3.2.

yes

62


4.2.1

Evaluating the partner proposal

The evaluation of an order / supply pattern proposed by the collaboration partner can be accomplished by the intra-domain planning model as introduced in section 3.1.2, enhanced by links to adjacent domains. From the buyer’s perspective we expect that the supplier has announced supply quantities XSj,t by item and period for all supply items pertaining to the index set JS. In order to incorporate these quantities into local planning, the buyer can use Model 1 extended by constraints (10) to (13) as described in section 3.1.3. The resulting planning model is presented in Model 2.161 Model 2. CP(Buyer)-0 Formulation

min s.t.

c

(18)

(3) - (9) T

c=∑

∑ (ch j i j ,t

t =1 j∈J

T

+cf j y j ,t ) + ∑

is j ,t −1 + xs j ,t =

T

∑ cor or ,t + ∑ ∑ ch j is j ,t

t =1 r∈R

+ is j ,t ∑ r x k∈S j j ,k k ,t

t =1 j∈JS

∀j ∈ JS , t

(19) (20)

xs j ,t = XS j ,t

∀j ∈ JS , t

(21)

IS j ,t ≤ is j ,t ≤ IS j ,t

∀j ∈ JS , t

(22)

Proposed supply quantities XSj,t are input to the model due to constraints (21). However, as explained in 3.1.3, inventory holding of supply items is permitted. The objective is to minimize costs of local operations in conjunction with inventory holding of supply items ((19)). Constraints (3) to (9) pertain to Model 1 and correspond to balance equations, capacity restrictions, setup constraints, and bounds on variable values. Solving Model 2 reveals the cost optimal local plan given the supply quantities as proposed by the supplier. Model 3 depicts the equivalent situation for the supplier. Here, order quantities XOj,t by item and period as received from the buyer are incorporated into the intradomain planning model. It corresponds to Model 1 extended by constraints (14) and (15). Order quantities XOj,t are input to the model due to constraints (26) and represent demand in the modified balance equations (25).162 Solving the model hence

161 162

For a description of the symbols see Model 1, p. 33, and section 3.1.3, p. 35. The original demand parameters Ej,t are still present, as the supplier may also serve other (external) sources of demand. The same set of supply items JS is used in both buyer and supplier models as the items ordered by the buyer and those supplied by the supplier are identical in a two-partner scenario.


63

reveals the cost optimal local plan based on the order quantities as proposed by the buyer. Model 3. CP(Supplier)-0 Formulation

min s.t.

c

(23)

(3) - (9) T

c=∑

∑ (ch j i j ,t

t =1 j∈J

T

+cf j y j ,t ) + ∑

i j ,t −1 + x j ,t = E j ,t + xo j ,t +

∑ cor or ,t

(24)

t =1 r∈R

∑ r j ,k xk ,t + i j ,t

∀j ∈ J , t

k∈S j

xo j ,t = XO j ,t

∀j ∈ JS , t

(25) (26)

In summary, the presented models can be used to find the optimal local plan based on received supply or order quantities. The optimal solutions to the models thus can be used to evaluate a partner proposal. The corresponding optimal costs c* is in every case greater than (or equal to) the cost resulting if a deviation from the partner proposal is permitted to some degree. Therefore, we will refer to it as C Bmax = c*, C Smax = c *

(27)

for the buyer and supplier, respectively. 4.2.2

Determining the preferred outcome

The purpose of this second step is to find all modifications to the received order / supply pattern which improve the local cost situation. Therefore, deviations from the received pattern are permitted and desired. Resulting is the most preferred order / supply pattern that can be devised from the one just received from the collaboration partner. The original and the most preferred pattern form the basis for finding the compromise solution proposed to the collaboration partner. A key question in obtaining the most preferred order/ supply pattern is whether there are some limits to deviations from the partner’s proposal. In fact, some kind of limits are required. Although their specification is discussed shortly, we assume for the moment that some limits exist and are known at this stage of the process. As can be expected, the planning models presented in the previous section can be used to determine the preferred outcome after introducing a few extensions. The resulting, modified model for the buyer is given in Model 4. Model 4. CP(Buyer)-1 Data min XScum, minimum cumulated supply quantity of j in periods 1 through t j, t

max maximum cumulated supply quantity of j in periods 1 through t XScum, j, t

ε

arbitrarily small number ( 0⎪ min = XScum, ⎨ cum ⎬ j, t else ⎪⎩XS j, prev t −1 ⎪⎭

∀j ∈ JS , t

69

(47) (48)

Finally, if both minimum requirements from final demand and rule-based shifts are available to the supplier, the ultimate minimum quantities have to be computed as min min min XO ′j,cum, = max XO cum, , E cum, ∀j ∈ JS , t (49) t j, t j, t

{

}

such that they correspond to the tighter of the two bounds. 4.2.3

Generating a compromise proposal

The minimum cost solution obtained above contains all modifications (within the defined limits), which yield a decrease of local cost. Among those modifications some are more effective than others, i.e. some incur significant marginal savings while others only have a minor impact on cost. In terms of the negotiation metaphor, the order / supply pattern corresponding to the minimum cost solution represents a “maximum claim”, that is a counter proposal which could not be better from the local perspective. However, real life examples show that maximum claims often are unacceptable to negotiation partners. The same principle applies here: Since modifications tend to increase cost for the collaboration partner, his cost increase will be the higher, the more modifications are present in the counter proposal. Therefore, only modifications with high impact on local costs should be included in a compromise proposal. These most effective modifications also offer the greatest chance among all of them to improve the overall cost outcome (assuming that all modifications cause comparable per-unit degradations for the partner). The following section discusses methods of finding effective compromise proposals. Thereby, we can make use of the planning models shown above, once more in somewhat extended versions. 4.2.3.1

Model-based methods for finding compromise proposals

The purpose of this process step is to find an order / supply pattern with only few, but highly cost effective modifications. The optimal compromise proposal is one which offers maximum cost savings (vs. the cost associated with the partner proposal) per unit deviation from the original order / supply pattern. This objective can be formally expressed as (50) max (C max − c) d where d corresponds to a measure of the total deviation (or degree of modification).

70


The interdependence between cost savings and deviation is visualized by an example in Fig. 16.166 The diagram shows the functional relationship between the deviation from the original pattern (expressed in terms of a percentage measure167) and relative cost savings, i.e. associated savings Cmax-c divided by the maximum savings potential Cmax-Cmin (curve “relative savings”). It can be seen that, in this example, savings first occur at an almost constant rate, followed by a steep increase around a deviation of 0.1. Thereafter, the marginal effect of additional modifications steadily declines. Also shown is the ratio between relative savings and deviation. It has its maximum in the region with largest incremental savings. Thus, the solution at a deviation of about 0.1 represents the optimal compromise proposal in this example.

2.5

Relative Savings

[100%]

2

Rel. Sav. / Rel. Dev.

1.5

1

0.5

0 0

0.2

0.4

0.6

0.8

1

Total deviation d

Fig. 16. Interdependence between savings and deviation

In order to obtain compromise proposals with the planning models presented above, following modifications are required: With a new variable d we can derive an extended model formulation by replacing the objective function with (50). Also, an extra constraint has to be added for the calculation of the total deviation measure d. Solving the resulting model then yields the optimal compromise proposal.

166

167

The example was obtained from a test instance by parametric optimization, i.e. restriction of the maximum deviation to an incrementally increased upper bound of x%. The precise definition of d is develop in the next section 4.2.3.2.


71

However, the objective function based on (50) is non-linear, converting the model into a non-linear programming problem of the type (51) f (x) max (52) g i ( x ) ≤ bi ∀i = 1..m s.t. where f and gi are given functions. 168 If d is computed linearly, then the constraint set remains linear and can be rewritten as Ax ≤ b (53) where A represents the matrix of coefficients and b the column vector of values bi. Since the objective is in the form of a fraction, the model more specifically corresponds to a fractional programming problem.169 Unfortunately, non-linear programming problems are in general difficult to solve and a standard solution algorithm as for LP and MIP is not available.170 A heuristic which could potentially be applied to the resulting fractional program is Successive Linear Programming (SLP).171 This method is “a differential technique which utilizes the linear programming algorithm repetitively in such a way that the solution of the linear problem converges to the solution of the non-linear problem”.172 However, applying SLP to the model regarded here poses difficulties. For one, there is a need of differentiability of the objective function in all variables. Since the model may contain binary variables, this is not given. Second, even if this could be resolved, SLP algorithms are complex and require a large number of iterations to obtain satisfactory solutions.173 Because of these issues and since it is not crucial to find the truly optimal solution for our purpose of generating a good compromise proposal, we will not try to make use of SLP for solving the non-linear program. Instead we utilize an approximate approach which is easier to implement. It grounds on the idea to consider the numerator and denominator of (50) as two separate objectives, i.e. 1) maximize cost savings and 2) minimize the amount of modifications.

168 169

170

171

172 173

C.f. Hillier / Liebermann (2001), p. 654. C.f. Hillier / Liebermann (2001), p. 669. Fractional programming problems with an objective function of a special type can be converted to linear programs by a variable substitution (c.f. Neumann / Morlock (1993), pp. 575). However, the above fractional program does not satisfy the necessary conditions (e.g. non-zero denominator values in the entire feasible region). C.f. Domschke / Drexl (1998), p. 165. Specific solution methods only are available for special problem structures such as the “Modified Simplex Method” for quadratic programming problems (c.f. Hillier / Liebermann (2001), pp. 686). Also called Method of Approximation Programming (c.f. Griffith / Stewart (1961), p. 379). Griffith / Stewart (1961), p. 379. Zhang et al. (1985) observe an average of several hundreds for some problem structures in their computational study.

72


Then, instead of maximizing the ratio according to (50) a simultaneous optimization of the two (conflicting) objectives can be pursued. A widely used technique for dealing with multiple objective optimization is goal programming which can be applied here, too. The term goal programming (GP) was coined by Charnes / Cooper (1961) who have developed the method in order to solve infeasible linear programs with a minimum violation of the problem constraints.174 Since then numerous authors proposed GP models in dealing with various types of multiple objective problems.175 GP comprises the specification of target values for the respective goals and the formulation of a (linear) programming model which minimizes deviations from the pre-set target values. GP models can be classified into two subsets: models which aim at minimizing the (weighted) sum of deviations from all goals and models with priorities for goals.176 Only the first type is considered in the following. The standard model formulation is as follows:177 K (54) min ∑ ( win ni + wip pi ) i =1

(55) x ∈ CS (56) ni ≥ 0, pi ≥ 0 ∀i = 1..K (57) where x is a vector of variables and fi(x) are (linear) objective functions with target values Bi. Non-negative variables ni and pi measure negative and positive deviations from the target values which are minimized in the objective function. Parameters wni and wpi represent (optional) weights attached to the respective deviations. Cs is the set of hard constraints which defines the problem’s feasible region. Depending on the value domains of variables x, the GP model is an LP or MIP and can be solved to optimality by standard Simplex or Branch & Bound algorithms. Its optimal solution exhibits the minimum weighted sum of deviations from the target values. Thus, it represents the optimal compromise between the conflicting objectives. An important issue of GP models is so-called incommensurability. It means that different units of measure may be used for the individual goals and their target values. In result “the relative magnitudes of measures taken from differing populations […] bias the solution process in favor of the parameters what will yield the largest reduction in deviation”.178 To counteract, a normalization of the deviations is required.179 The most intuitive normalization procedure utilizes the target values s.t.

174 175

176 177 178 179

fi ( x) + ni − pi = Bi

∀i = 1..K

C.f. Charnes / Cooper (1961), pp. 215, Cooper (2002), pp. 36. C.f. Aouni / Kettani (2001), p. 225. See e.g. Schniederjans (1995), pp. 73, for an overview. C.f. Tamiz et al. (1998), p. 570. C.f. Tamiz / Jones (1996), p. 299. Schniederjans (1995), p. 28. C.f. Tamiz / Jones (1996), p. 202.


73

as normalizing constants (called “percentage normalization”). In result a revised GP objective function is obtained of the form (58) K wn wp min ∑ ( i ni + i p i ) Bi

i =1

Bi

With this extension in place all deviations contribute with the same order of magnitude to the GP objective function.180 With regard to finding a compromise order / supply pattern, a GP model can be devised from the conflicting objectives stated above. However, objective one (“maximize cost savings”) has to be reformulated in order to define a reasonable target value. Since we know the that minimum possible costs are Cmin, minimizing the deviation from Cmin rather than maximizing savings vs. Cmax forms the first objective. The target values hence correspond to minimum cost Cmin for the cost savings objective and zero for the deviation objective. As both goals are measured in different units, an appropriate normalization is needed. Resulting costs c can take values between Cmin and Cmax, so that the interval (Cmax-Cmin) can be used to normalize deviations to values between 0 and 1. Likewise, we assume that the measure of total deviation is normalized to the 0-1 interval (its precise definition is derived in the next section). The resulting GP model for the buyer is presented in Model 6. Model 6. CP(Buyer)-2 Data Cmax maximum cost (CP-0 solution) Cmin minimum cost (CP-1 solution) WC weight of cost objective WD weight of modification objective Variables ∆ deviation from minimum cost d percentage modification of supply pattern Formulation min

s.t.

WC C

max

−C

min

∆ +W D d

(59)

(3) - (9), (29) - (34) d = f ( XS j ,t , xs j ,t ) c−∆=C

min

(60) (61)

Except for the objective function and the additional constraints (60) and (61), the model is equivalent to Model 4. (60) and (61) capture the deviations from the target goal values. Since the definition of the modification measure follows below, (60) only indicates that the total distance d is calculated from original and current

180

It should however be noted that percentage normalization requires non-zero target values Bi.


74

supply quantities. The deviation variable ∆ captures the cost increase above Cmin. The objective function contains the weighted sum of the target value deviations. As explained above, ∆ is normalized by the interval width of (Cmax-Cmin). The weight parameters are discussed in more detail below in section 4.2.3.3. The corresponding supplier model is obtained identically from Model 5, only that deviations from order values (XOj,t) are considered here. The formulation is given in Model 7. Model 7. CP(Supplier)-2 Formulation min

s.t.

WC C

max

−C

min

(62)

∆ +W D d

(3) - (9), (36) - (40) d = f ( XO j ,t , xo j ,t )

(63) (64)

c − ∆ = C min

Solving the GP models does not guarantee maximization of the original objective according to (50). However, it produces a compromise close to the maximum, as it contains only those modifications which have a higher impact on cost savings than on the deviation measure. The optimal GP solution represents a compromise where cost savings and deviations are balanced one vs. the other. 1

Goal programming objectives

0,9

∆% + d

0,8 d

∆%

0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 0

0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 Total deviation d

Fig. 17. Relationship between goal programming objectives

1


75

The situation is visualized in Fig. 17 for the same example as considered above in Fig. 16. It shows the conflicting relationship of the two objectives and how ∆% (the normalized cost increase above Cmin) decreases with growing deviation d. Also shown is the sum of the two target value deviations (∆%+d). As can be seen, the sum takes its minimum at a deviation d of about 0.1, right in the vicinity of the maximum to the original objective according to (50). Applying the above GP models is an efficient way to generate compromise proposals, as we obtain the compromise order / supply pattern by solving a single additional planning model. Also, the method can be easily extended such that additional compromise proposals are generated, a feature which will prove useful shortly. Irrespective of the method used to obtain a compromise proposal, the total amount of modifications present in the compromise is smaller than in the minimum cost solution to Model 4 / Model 5. This is depicted in Fig. 18 for the supplier. It shows received cumulated order quantities (XOcumj,t), and cumulated order quantities obtained with Model 5 (xocum,1) and Model 7 (xocum,2). As indicated, the solution of Model 7 is closer to the original order pattern, because only a part of all possible modifications is contained in the compromise. The savings realized with the compromise are (65) ∆C = C max − c * when c* is the cost associated with the compromise solution. The definition of the deviation measure d, which has been deferred so far, is described in the following section. XOcum / xocum XOcum xocum,1

xocum,2

t Fig. 18. Cumulated original and compromise order quantities

4.2.3.2

Distance measure for order / supply patterns

Based on the definition by Jain et al. (1999) “a distance measure is a metric (or quasi-metric) on the feature space used to quantify the similarity of patterns”.181 Distance measures are for example used in Cluster Analysis where they are

181

Jain et al. (1999), p. 270.

76


needed to identify similar objects which can be grouped to a cluster.182 Similarity is usually determined from a set of parameters xj of the objects considered. Generally, parameters can have discrete or continuous value domains, however only the latter are of relevance in the following. Given two objects k and h with continuous parameter vectors xk, xh of dimension N, the Minkowski metric 1/ P (66) ⎡N ⎤ d k ,h = ⎢ ∑ x kj − x hj ⎢⎣ j =1

P

⎥ ⎥⎦

is often used as a measure of the dissimilarity or distance between the objects.183 Most popular are the first and second order cases (P=1, P=2). The first is the socalled City-Block Metric or L1-norm while the latter represents the Euclidean distance or L2-norm between the points xh and xk in ℜ N space.184 Similar as goal deviations in GP models, varying magnitudes of parameter values have a distorting impact on the contribution of individual parameters to the total distance measure. Therefore, appropriate normalization is required to balance the effects of various parameters. For the generation of compromise order / supply patterns, the amount of modifications or the total deviation from the received proposal has to be determined. Hence, the set of parameters distinguishing alternative patterns is made up by cumulated order or supply quantities xoj,tcum / xsj,tcum. Furthermore, since the distance measure is incorporated into the GP models, a linear distance calculation is required, making the L1-norm introduced above the obvious choice. The question however is how individual parameters can be appropriately normalized and combined to a total distance. First, we can sum up all parameters pertaining to a single item, as they are expressed in identical unit measures. The absolute item-specific deviation measure hence is calculated for the buyer as185 (67) d ABS = XS cum − xs cum ∀j ∈ JS j

∑

t∈T

j ,t

j ,t

The definition in (67) can be further simplified, if we recap that shift quantity variables d-j,t/d+j,t link received proposals XOj,t / XSj,t and the respective variables xoj,t / xsj,t.186 Due to the corresponding balance equations the values of shift quantities d-j,t/d+j,t represent the cumulated excess or short supply vs. the original proposal. Therefore, the difference term in (67) can be replaced by the sum of shift quantities to previous and next periods, yielding187 182 183 184

185

186 187

C.f. Backhaus et al. (1996), p. 264. C.f. Hartung / Elpelt (1995), p. 72, Jain et al. (1999), pp. 271. C.f. Backhaus et al. (1996), p. 274. The Euclidean distance resembles the length of a connecting line between the points xh and xk in two and three dimensional space. The calculation for the supplier is equivalent but based on cumulated order quantities XOcumj,t. See e.g. constraints (31) of Model 4, p. 64. Mathematically, we have from constraints (31)

4.2. Iterative Planning Steps d ABS = j

∑ (d +j ,t + d −j ,t )

77

(68)

∀j ∈ JS

t∈T

The total item-specific quantity can then be normalized by the maximum shift quantity Djmax contained in the most preferred, minimum cost solution to Model 4 / Model 5.188 Resulting is an item-specific percentage deviation according to dj =

d jABS D max j

=

∑ (d +j ,t + d −j ,t )

t∈T

(69)

189

D max j

In a second step, the item-specific percentage measures have to be combined to a single, overall distance. The natural approach to accomplish this task is by averaging item-related values. Using a simple arithmetic mean (i.e. the sum of itemspecific measures divided by the number of items), the total distance is d=

1 JS

∑d j

(70)

j∈JS

However, the above calculation can result in a misleading total distance, because it ignores the relative importance, e.g. total order volume, of individual items. As an example let us consider a two-item case with 100% distance for one item and 1% for the other. The mean distance here is 50.5%. However, if the first item is perceived much more important than the second, one would intuitively attach a higher total distance to this scenario. Vice versa, if item one is considered miscellaneous compared to item two, a smaller total distance seems appropriate. To incoporate this, a weighted average of the form d=

∑ wjd j

∑

=

j∈JS

j∈JS

wj ⎛ ⎞ ⎜ (d +j ,t + d −j ,t ) ⎟ ⎟ max ⎜ ∑ D j ⎝ t∈T ⎠

(71)

can be used. Assigning weights however requires a careful assessment of the consequences. in order to avoid so called “naïve relative weighting”, i.e. a situation where chosen weights do not accurately reflect the true proportional importance.190 Two ways of XS j ,t − xs j ,t = d +j ,t + d −j ,t − d +j ,t −1 − d −j ,t +1 and hence cum XS cum j ,t − xs j ,t =

=

d +j ,t

t

∑ ( XS j , s − xs j , s )

s =1

− d −j ,t +1 + d −j ,1 − d +j ,0

=

d +j ,t

=

t

∑ (d +j , s + d −j ,s − d +j , s −1 − d −j , s +1)

s =1

− d −j ,t +1

= d +j ,t + d −j ,t +1

(the last two simplifications are valid because d-j,1=d+j,0=0 by definition and only one of d+j,t or d-j,t+1 is greater than zero at any one time). Thus, we obtain cum ∑ XS cum j ,t − xs j ,t

t∈T 188 189 190

=

∑ (d +j ,t

t∈T

+ d −j ,t +1 ) =

∑ (d +j ,t

t∈T

+ d −j ,t )

(the last transformation is possible given that d-j,1=d-j,T+1=0). See equation (42), p. 66. If Djmax equals zero, a small number ε (

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