Parts management models and applications: a supply chain system integration perspective

Parts Management Models and Applications A Supply Chain System Integration Perspective

Parts Management Models and Applications A Supply Chain System Integration Perspective S ameer Kumar University of St. Thomas Minneapolis, Minnesota

Spriinger

ISBN 0-387-22821-7 ©2005 Springer Science + Business Media, Inc. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, Inc., 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed in the United States of America. 9 8 7 6 5 4 3 2 1 springeronline.com

Dedication

This book is dedicated to the Family, Parents and Friends

Preface

Parts are commonly used in making, repairing or maintaining consumer or industry products. Parts could be purchased or manufactured by a business enterprise. Advance models were applied to parts operations for manufacturers of transport refrigeration equipment and high-pressure positive displacement plunger pumps. Both companies have an established network of dealers for sales and service of equipment and parts. A number of areas in the parts business operation were researched which show the potential for improved operational efficiency and customer service that increase market share when advanced process models were used to integrate the supply chain. This book covers the subject of parts management through: (1) an introduction to areas of parts business operation with potential for substantial improvements and overview of various models proposed in Chapter 1; (2) quantitative effects on customer service level of inventory miscount and lead time variability and methods to reduce these factors in Chapter 2; (3) optimal division of items based on economics within a two-level distribution system; which items should be serviced through dealers and which items directly by the company to end-customers in Chapters; (4) optimal ordering procedures for a multi-item common supplier system with either constant or random demand rates for various items in Chapter 4; Vll

viii

Parts Management Models and Applications (5) attribute based classification scheme to promote standardization of design and manufacturing techniques for expediting product development and control design proliferation in Chapters 5 and 6; (6) knowledge base management to enhance manufacturing operations effectiveness in Chapter 7; (7) showcasing improvement in planning and fulfillment process of a manufacturing operation through integrated supply chain efforts in Chapter 8; and (8) summative understanding of the significance of holistic approach to parts management and presenting various aspects of successful Dell Computers Supply Chain.

The book attempts to present a detailed overview of management of parts operation whether it relates to procurement, engineering design, manufacturing, warehousing or distribution. It also makes emphasis on the combined look at all business functions of a company including working closely with major suppliers and customers.

Acknowledgments

The book is the blending of author's research interests and twenty plus years' experience working in industry on projects relating to Parts Supply Chain Optimization. The holistic view described in "Parts Management Models and Applications" book is adapted from published papers focused on various aspects of parts management covering: procurement, design, manufacture, inventory, distribution, customer service and the entire value chain. The major contribution of the book comes from a number of models developed, viewpoints and industry applications for managing parts business operation in a supply chain context. I have acknowledged the citation of the adapted work published in professional literature as end notes at the end of various chapters in the book. I am indebted to my family, parents and friends for their unconditional support. I also wish to thank the editor and the entire production team at Springer for their assistance and guidance in successful completion of this book. Sameer Kumar Minneapolis, Minnesota

IX

Contents

Chapter 1 - Introduction To Parts Management

1

Chapter 2 - Inventory Miscount & Lead Time Variability - Effects & Control Mechanisms? Chapter 3 - Optimal Division Of Items Within A Two-Level Distribution System

49

Chapter 4 - Optimal Ordering Procedures For A Multi-Item Common Supplier System

69

Chapter 5 - Parts Proliferation And Control

99

Chapter 6 - Economic Viability Of Component Management For A New Product Design! 17 Chapter 7 - Manufacturing Operations Effectiveness Through Knowledge Based Design 133 Chapter 8 - Serve Your Supply Chain, Not Operations

155

Chapter 9 - Holistic View Of Parts Management

189

Appendices

199

References

205

Index

219

xi

Parts Management Models and Applications A Supply Chain System Integration Perspective

Chapter 1 INTRODUCTION TO PARTS MANAGEMENT

This book deals with management of parts business operation covering such issues as, their procurement, design, manufacturing and distribution to ultimate customers. Various models are described and their applications shown using examples of a leading manufacturer of transport refrigeration equipment and a manufacturer of high pressure positive displacement plunger pumps. These companies have established network of dealers for sales and service for both equipment and parts. Majority of the parts are purchased from other manufacturers. The parts market is very competitive. Both price and customer service, are important factors in determining the market share. The focus of this research is to improve customer service; reduce costs through improved inventory and operational management techniques; and address improvements in supply chains and not on individual business operations in a company.

1.

POTENTIAL AREAS OF IMPROVEMENTS

After a preliminary study of the system, the following areas were selected where potential for substantial improvements existed using the examples of above-mentioned companies. Inventory Count and Procurement Lead Time Errors in inventory count affect ordering decisions and consequently customer service level. If reported inventory count for an item is smaller than its actual inventory, extra inventory will be carried all the 1

2

Parts Management Models and Applications

time. If reported inventory count is larger than the actual inventory, the ordering for the item will be delayed and more stockouts will result than planned through the model. Procurement lead time is an important factor in ordering decisions. Usually lead times are assumed to be constant in inventory decision models, as variable lead times models become somewhat more complex. However, ignoring lead times variability, when it is substantially sizeable, can have a devastating effect on customer service. The ordering procedures in the company treats procurement lead times as constants when they are indeed variable. The management has been concerned about both the accuracy of the inventory counts and about the variability of the lead times not being considered in ordering rules. Chapter 2 covers three major themes. The first deals with developing quantitative effects of inventory miscount and non-incorporation of lead times variability in ordering rules on Customer's Service Level individually and jointly. Development of Procedures for Reducing Inventory Miscounts The sources of errors were found to be primarily due to data entry. These errors persisted for long times in the system. There were no formal procedures to identify these errors and correct them. The second theme in Chapter 2 deals with developing parity checking procedures based on material conservation concepts at the micro level, for identifying and correcting data entry errors during receipts and issues of materials. The micro-level implementation of the conservation equation required development of a coding scheme for tracking the flow of materials during their transient stages. The checking for the compliance of the audit procedure is done on an ongoing basis by a simple physical inventory program. Implementation of EDI Communication Network with Suppliers to Reduce Lead Times Variability Electronic Data Interchange (EDI) as a technology has been proven to reduce procurement lead times and ordering costs substantially. The third theme in Chapter 2 deals with presenting an explicit relationship between EDI and JIT. A simple model illustrates how lot sizes can become smaller with EDI network. It emphasizes and quantitatively shows that any reductions sought in lot sizes without a genuine reduction in ordering cost and lead times would impose penalties instead of achieving economies. EDI network lowers inventories and safety stocks.

Introduction to Parts Management

Optimal Division of Items within a Two-level Distribution System Two-level distribution systems are common as was the case in the company studied. Expensive and low demand items were presumed serviced directly by the Company, whereas other items distributed through dealers. The existing division of the items is more or less on a subjective basis. It was commonly felt within the company that dealers should keep shelf inventory for more items. They made their decision regarding whether an item should be on shelf or not, on an individual basis. If an item is not profitable, they would not inventory it. Chapter 3 gives an economic rationale for subsidizing dealers to encourage them to keep shelf inventories for more items. The subsidization is justified on account of the resulting increased market share and profitability. This Chapter develops a rational basis for deciding which items should be serviced through dealers and which items directly b)^ the company. Management has been debating this issue for a long time. Development of More Appropriate Lot-sizing Rules for Common-supplier Cases Existing ordering rules were based on the assumption of separability of the objective function on an item basis and the traditional EOQ models were being used. In reality, several items had a common supplier. The ordering cost, while ordering from a common supplier, had two components - a major common part "A", which was independent of the number of items ordered and a minor component "a" which linearly increased with the number of items. Chapter 4 develops lot-sizing rules for constant and random demands for various items. The first part of Chapter 4 develops optimal ordering procedures for a multi-item system supplied by a common supplier, with constant demand rates for various items. The model presented in this Chapter allows for planned stockout levels, computed on the basis of the total cost minimization. The second part of Chapter 4 deals with heuristic ordering rules for multi-item single supplier case with random demands. The assumption of constant demand rate may not be valid in certain cases where demand variability is sizeable. The ordering rules developed in this chapter include when to order and which items to order. An order is placed when composite stockout cost rate exceeds a multiple of the average ordering cost per order. Appropriate values of the parameters used in operational management rules are determined by minimizing the total variable cost.

4

Parts Management Models and Applications

Parts Proliferation and Control As is typical in any parts inventory system, there were lots of items in the inventory very similar to each other and interchangeable. No formal procedures existed to control the proliferation of parts. The valid point for controlling this proliferation was the Design Department. It was here where decisions to add new parts were taken. One of the procedures for controlling parts proliferation is to provide the design engineer with a list of parts similar to the new part that he is planning to design, for his perusal and evaluation as to whether one of the existing parts can be a substitute. Chapter 5 develops a classification scheme to form and retrieve a subset of items similar to the new proposed design. The classification scheme is attribute based. A finite number of attributes characterize an item. The selected attributes for variety control purposes are the ones that relate to various design characteristics. The Principal Components Analysis technique is used to generate principal components, where a fewer number of components would explain a major portion of total variance in the values of the attributes. The grouping of the items on design similarity criterion is done hierarchically using these principal components. Chapter 6 explores the viability of standardization of design and manufacturing techniques to expedite product development and control design proliferation using an example of a leading transport refrigeration unit manufacturer. An incremental approach to implementing standardization in a product development environment using a conceptual framework for component management decision support system is presented to build a case for its technical feasibility. The primary objective of this chapter is to provide an economic justification for implementing the proposed system. A three level decision making hierarchy is proposed with economic optimization for levels 1 and 2 representing standardization of system modules and capacity decisions for a product line respectively. Thermodynamic optimization for level 3 represents control systems to keep the system dynamically balanced in changing environments. Other potential applications amenable to classification are identified. Enhancing Manufacturing Operations Effectiveness Through Knowledge Based Design Chapter 7 is based on the realization that global competition has pushed firms to continuously improve and upgrade their manufacturing operations. Role of knowledge base and learning to facilitate this phenomenon are explored. Developing a knowledge base requires organizing knowledge and expertise for a field of inquiry and making it

Introduction to Parts Management

5

available in formats suitable for users to support and aid various operational, developmental, and organizational functions. Classification and coding form the basis for organizing knowledge bases. Most classification schemes are attribute based. Classification implies grouping objects into similar classes on the basis of some similarity criteria pertinent to one or more attributes. Learning in the context of classification implies discovering new attributes, bases for grouping and requires frequent updating of the knowledge base. When a system evolves, ideally so should its knowledge base and classification scheme. A formal knowledge base makes a firm's knowledge cumulative and serves an important integrating and coordinating role for the organization. These concepts have been applied to support manufacturing activities at a leading, transport refrigeration unit manufacturer. An example application utilizing classification as a tool for knowledge acquisition in design support activities at this firm is presented. Serve Your Supply Chain, Not Operations Chapter 8 describes a pilot study carried out to improve planning and fulfillment process in a division of a manufacturer of high-pressure positive displacement plunger pumps. The focus was to develop a synchronized system from source to consumption with continuous flow of information and materials for one of this division's main product lines. System-wide changes were accomplished using a cross-functional team with the goal of reducing waste and investment in inventory. Traditional measures of manufacturing efficiency and utilization were compared to proposed measurements of throughput (T), investment in inventory (I), and operating expense (OE). Although traditional measures showed actual decline; proposed measures showed improvement and increased profitability of 200% for this product line. These new performance measures reflected a change from local to global thinking. Improved capacity management in the system was achieved by sharing information between suppliers and customers. Holistic View of Parts Management Chapter 9 summarizes understanding of total parts management. It also describes a highly successful Dell Computers supply chain. In this supply chain, the company closely matches product demands with manufacturing of products and procurements of parts from suppliers.

6

Parts Management Models and Applications

The approaches outlined in this book were used to adapt simple models to accurately address complex operational dynamics. The holistic approach to synchronizing systems from source to consumption has resulted in increased profitability, improved customer service and well coordinated business operations. These new advanced models described in the book are not limited to industries studied but have general applicability.

Chapter 2 INVENTORY MISCOUNT AND LEAD TIME VARIABILITY - EFFECTS AND CONTROL MECHANISMS

This chapter consists of three major sections; each has a focus on different aspect of inventory performance management system. The first studies the quantitative effects of inventory miscount and non-incorporation of lead time variabihty on customer sen^ice level and on the inventory holding cost in a parts management system. An inventoiy miscount for an item implies a discrepancy between its actual physical inventory count and its quantity as per computer records. Tlie second section focuses on schemes to reduce inventoiy miscounts from the operational management point of view. The third section illustrates how EDI networks lower both ordering costs and lead times and consequently result in smaller lot sizes and smaller safety stocks.

1.

INVENTORY MISCOUNT AND LEAD TIME VARIABILITY

This section establishes the need tbr developing procedures for reducing inventory miscounts and for incorporating the level of miscounts along with the lead times variability in tlie computation of reorder points.

8

1.1

Parts Management Models and Applications

Introduction

The importance of short delivery times for spare parts has been widely stressed in the professional literature (Duchessi, Kumar and Levy 1988; Ronen 1983). The impact of lead time variability on the total system cost has also been extensively studied (Buchanan and Love 1985; Gupta 1979; Lau and Zaki 1982; Magson 1979). The study originatedfromthe management commitment to raise customers' service level without further increasing investments in inventories. The company manufactures and also services transport refrigeration units. The chapter focuses on the parts distribution portion of the business. The Service Parts System has approximately 45,000 parts. About 80% of the parts are purchased and the remaining 20% manufactured by the company. Approximately 10%) of the manufactured parts are contracted out to specialized vendors and they are provided witfi a major portion of the needed components and raw materials. About 95%) of the yearly sales of service parts are from one-third of the parts. Exponential smoothing techniques with trend are currently being used to forecast future demands. A fixed lead time, subjectively determined, is assigned for every part. The reorder points are based on the average lead time demands and the management prescribed service level. However, the actual service level realized falls far below the prescribed service level on which the reorder points are presumably based. The consistently lower realized service level has been a puzzling problem for the management for some time. The diagnostic steps carried out suggested that the two main causes for the lower realized values of the service level were: (i) Miscount in the inventories of the parts, and (ii) Non-inclusion of lead time variability in computing reorder points. The magnitudes of their effects are assessed through the following model.

1.2

The Model Quantifying Effects on Service Level^

We begin with describing the notations used in the proposed model.. Notations The following notations for each item j have been considered. (The index j is subdued in the development of the model.) t = When t is used as a suffix of a variable, it denotes the value of the variable at time t, I^ = Inventory on hand as per computer records, I^ = Actual physical inventory on hand.

Introduction to Parts Management Wt At /' Q R P

= = = = = =

P D^ D L cr^ a^ (7^ K K h_ L I

= = = = = = = = = = = =

On-order quantity, Inventory already allocated but still in stock, Inventory position as per computer records, Order quantity, Re-order point, Fraction of the demand desired to be met, from the shelf inventory, also called service level, Actual service level realized, Demand rate, Average demand rate, Procurement lead time, Standard deviation ofdemand over lead time, Standard deviation of demand rate, Standard deviation of lead time, Safety stock factor used in computing reorder point. Effective safety stock factor, Holding cost per unit item per unit period, Average lead time, Relative error in on-hand inventory given by

(i{t)-i{t))/m, fit)

= Probability density function of I,

i (T; HL = Probability density function of

G,{K)=l{U-K)cl>[u)dU, where ^(f/)denotes the density function of a unit normal distribution.

EFFECT OF INVENTORY MISCOUNT The ordering decision for an item is based on the Inventory Position It', where

i;=i,+w,-A,.

(1)

10

Parts Management Models and Applications As shown in Figure 2-1, a quantity Q is ordered when It' (Inventory Position based on computer records) hits the reorder level R. The actual service level realized is affected by the deviation of I^ (the actual physical inventory)fromIt (on-hand quantity as per computer records). It is assumed that demand follows a normal process. The demand during lead time L will follow a normal distribution with mean DL and variance cr^ . Its densityfiinctionis denoted by^(x). If the lead time variability is duly considered, the reorder point R is given by

(2) where

(3) and K is the safety stock factor. Assume that the management prescribes a service level P, where P denotes the fraction of the demand desired to be met from the shelf inventory (say, P is 0.95. as an example). As per management's prescribed service level, the total average demand over an ordering cycle duration that may not be metfromthe shelf inventory will equal

Q{l-P)

(4)

Introduction to Parts Management

11

\y/

Figure 2-1. Illustrating reorder point and ordering procedure

Tlie truncated mean of a normal distribution ^(x) with mean DL and 2

variance GJ>, is given by

[{x-R)l>{x)dx. This measures the average demand per ordering cycle not met from shelf inventory. Substituting \x - DLj/ GJ^ = U, the above integral becomes

/^.

Casel. / / / r In this case, the actually realized service level P will fall below the planned service level P. The value of P is given by G^ ((/, + PF, - 4 - D Z ) / c r ^ J = 2(1 - P) / cTo,. Recall that the relative error in inventory miscount is denoted by

(9)

Introduction to Parts Management

13

The values of P for various values of P and t are given in Table 2-1. These values are plotted in Figure 2-2. The calculation of P in the previous section assumes a constant lead time ( a L = 0). The calculations for variable lead times are given in the following section. These tables are based on a typical item with the following parameter values:/) = 451.6, cr^ = 377.2, L = 2.04, o-^ =0.77, Q=1420.

Table 2-7. Values of P for Various Values of P and £

^\^^

£

P ^ " ^ ^ .85 .90 .95 .96 .97 .98 .99

.1

.2

.3

.4

.5

.6

.82 .87 .93 .94 .95 .96 .98

.78 .83 .89 .90 .92 .94 .96

.73 .78 .85 .86 .88 .90 .93

.68 .73 .79 .81 .83 .85 .89

.63 .67 .73 .75 .77 .79 .83

.57 .61 .66 .67 .69 .71 .75

Parts Management Models and Applications

14

0J5 0.9

wv To, where L is the age of a control number, given by the difference between the current date and the date of initiation of the control number. Some control numbers may exit set Si with the miscount errors identified and corrected by Rule 1, and some control numbers in set Si will be transferred to set S2, as these get older than TQ. Rule 2 Each open control number in set S2 is checked periodically for each in-transit station individually for compliance with the equality condition of the total debits and the total credits. If the equality condition holds for each in-transit station, this control number is deleted from set S2. Rule 3 This rule is designed for identifying and correcting inventory miscounts at stock stations. If the depletion rate at any time exceeds a prescribed upper-bound value, a special count for that item is triggered. This upper bound for each SKU will be established from the variance of the historical demand rates. The above procedure is illustrated through an example. Example Figure 2-11 shows a simple material-flow network, where S is an external source station; A, B and C are internal in-transit stations; and D, E and F are internal stock stations. Table 2-10 shows actual material flow pertaining to a control number, whereas Table 2-11 shows the associated computer records for the flow. Some errors have been purposely introduced in the records to illustrate the working of the three rules.

Introduction to Parts Management

35

Table 2-10. Actual Flow

s Dr

A

Cr

Dr

10

10

B

Cr

Dr

4

4

C Cr

6

D

Dr

Cr

Dr

6

4

4

Cr

E Dr

Cr

F Dr

Cr

4

Figure 2-11. A Simple Material-flow Network with Different Types of Stations

Table 2-11. Data Entries for the Flow

s Dr

B

A

Cr

Dr

8

8

Cr

Dr

4

4

6

D

C Cr

Dr

Cr

Dr

6

4

4

Cr

E Dr

Cr

F Dr

Cr

4

A comparison of the entries in Tables 2-10 and 2-11 is given in Table 2-12. The control number referred to is an open control number, as all

36

Parts Management Models and Applications

debits and all credits are not equal for each of the in-transit stations A, B, and C. A check is then made for compliance with Rule 1. Table 2-12. A Comparison of the Entries in Tables 2-10 and 2-11

Actual flow pertaining to a control number (Table 2-10) |T A lot of 10 units originates from the external source station S and flows to the in-transit station A. 2. This lot is split into two sublots of 4 and 6. The sublet of 4 units flows from A to B and sublot of 6 units flows from A to C. 3. The sublot of 4 units flows from BtoD. 4. From the sublot of 6 units, 4 units flow from C to E.

Computer records with some induced errors (Table 2-11) 1. Erroneously S is credited for 8 units and A is debited for 8 units (instead of the actuallO units). 2. Station A is correctly credited for 4 unitsand B debited for 4 units to account for the flow of the sublot of 4 units from A to B. 3. Station A is correctly credited for 6 units and C debited for 6 units to account for theflow of sublot of 6 units from A to C. 4. Station B is correctly credited for 4 units and D debited for 4 units. 5. Station C is correctly credited for 4 units and station E debited for 4 units.

Rule 1 identifies an error condition at in-transit station A, as the total credits for the control number exceed total debits. This error is traced immediately and it is presumed that it is corrected. This control number still remains in set Si. At the end of time To, it is transferred to set S2. A check is made for compliance with Rule 2.This rule will not be complied with as long as the 2 units remaining at station C do not clear. Rule 2 is designed for internal control. It will keep a watch that all intransit inventory is ultimately accounted for and does not disappear. Rule 3 will identify and reduce inventory miscounts at stock stations.

7.3

Model for Cycle-counting Frequencies

Errors escaping the internal control system and resulting in inventory miscounts will be corrected at cycle counting. Inventory records for an SKU are reset to an error-free state immediately following its cycle counting. In this section a model is developed for determining optimal values for cycle-counting frequencies.

Introduction to Parts Management

37

Notations T denotes inter-cycle-count time. Ti denotes the average time during a cycle over which an item's inventory records are in error. During Ti one or more errors can occur. Ci denotes the average inventory-counting cost per count per item. C2 denotes the average penalty cost per time incurred during the error phase. This penalty cost may depend on the magnitude of the error. In this article, for simplicity, the penalty cost is assumed to be independent of the magnitude of the error. D denotes demand rate per unit time. Q denotes the economic lot size. a denotes the mean error-occurrence rate for the item, a is assumed to be proportional to D/Q, which measures the activity level for the SKU. 7.3.1

Model

It seems realistic to assume that inter-arrival time between two consecutive data-entry errors for an SKU follows an exponential distribution. The value of Ti is given by T

T^ = ^{T-t)e-''ae-''dt,

(1)

On simplification of (1), we obtain r^ = r / 2 +1 /(4a^'"') - 1 l{Aa)

(2)

The total unit-time cost C(T) is given as C(r) = Q / r + C 2 ( i ) / 0 ( l / r ) ( r / 2 + l/(4ae'"O-l/(4a)). The optimal value of T, denoted by T*, is obtained by setting dC(T)/dT = 0, and, solving for T*, we obtain

(3)

38

Parts Management Models and Applications

[2a(C,/C,)

+

i2a(C,/C,)(Q/D)-(2a(C,/C,)(Q/D)yy"]

x[(a-4a\C,/C,)iD/Q)]-\ (4) If data-entry error rate a is assumed to be proportional to D/Q, then a is given as a = Ka,(D/Q)

(5)

where K is a proportionality constant and a^ is a system error parameter. Substituting this expression for a in (4), we obtain T*=

[2Ka,(C,/C,)

+

(2Ka,(C,/C,)-(2Ka,(C,/C,)yy^']

x[(Ka,-4K'a,\C,/C,))(D/Q)r (6) In order to simplify the management of the cycle-counting function, similar items are grouped on the basis of the parameter values of C2/C1 and D/Q. Table 2-13 shows a company-wide item classification. The two entries in each cell of the table represent: (1) the number of SKUs in each category; (2) the optimal inter-cycle-count duration T* for the category, as obtained on solving equation (6).

Introduction to Parts Management

39

Table 2-13. A Company-wide Classification of Items on the Basis of the Values of the Parameters C2/C1 and D/Q - The Estimated Values of ^ Q =0.1 and C, = $2 are Used in Computing the Values of T*

r\.^^^ D/Q

0.05

Ca/cT"^^^^-^^ [5

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.50

0.60

300

275

250

225

190

175

160

140

100

50

28

23

20

18

17

16

15

14

210

200

160

140

110

85

75

45

53

34

10

250

220

27

17

14

12

10

9

9

8

8

7

15

225

200

160

180

140

120

90

65

60

40

18

12

10

8

7

6

6

6

5

5

20

175

180

150

160

120

100

80

60

50

35

14

9

7

6

5

5

5

4

4

4

25

150

150

145

140

100

90

70

50

45

30

11

7

6

5

45

4

4

3

3

3

115

120

140

130

90

70

60

45

40

25

9

6

5

4

4

3

3

3

3

3

100

100

120

110

70

60

50

40

30

20

8

5

4

4

3

3

3

2

2

2

90

80

70

65

55

50

45

35

20

15

7

5

4

3

3

3

3

2

2

2

75

70

60

55

50

45

35

25

15

10

6

4

3

3

2

2

2

2

2

2

65

60

50

45

40

30

20

12

10

5

5

3

3

2

2

2

2

2

2

30 35 40 45 50

_2

Estimated expected total system-wide cycle-counting and penalty cost per unit time, W, is given by (7) 7=1

Where j denotes a category in the item classification matrix given in Table 2-13 and J is the total number of classes. An important system parameter is the value of K in equation (5). Achieving a reduction in the value of K through improved internal control procedures and improved

Parts Management Models and Applications

40

cycle-counting frequencies is an important objective of operational management. Table 2-14 shows the estimated values of W for various values of K. These values are plotted in Figure 2-12. It was estimated that at the end of one year after the internal control and cycle-counting procedures were implemented, the value of K moved down from five to one. This resulted in an estimated annual saving of $1.02 million. Table 2-14. Total System Cost W per Unit Time for Various Values of K K

1

2

3

4

5

6

7

8

9

10

W($)

3,519

4,653

5,382

5,899

6,279

6,562

6,771

6,922

7,024

7,087

6

7

9

10

8.00 7.00 6.00 - 5.00 Z 4.00

^ 3.00 2.00 I

1.00 h 0.00 ^ 1 2

3

4

5 K

Figure 2-12. Plot of Total System Cost W per Unit Time against K

Introduction to Parts Management

8.

41

CONCLUSION - INVENTORY ACCOUNTING PROCEDURES

Inventory management systems are becoming more and more computer-based. Internal audit procedures which are capable of identifying data-input errors on a timely basis are becoming increasingly important. The proposed audit procedures would likely eliminate most of the data-entry errors related to inventory transactions during receipt and issue of the parts. The implementation of the internal audit procedure required a slight enhancement of the company's prevailing inventory transaction code. A computer-based program would check for the compliance of the proposed internal audit rules on an ongoing basis. It will generate a list of open control numbers. These control numbers will be checked for non-compliance with Rule 1. A timely tracing of these non-compliances would eliminate most of the errors. If open accounts do not clear out of set Si in a reasonable time period To , these will be transferred to set S2. A periodic list of accounts in set S2 will force more accountability as a result of Rule 2 for the material flow within in-transit stations. The scope for pilferage will decrease significantly. Any data-entry errors for stock-station transactions will be identified and corrected as a result of Rule 3. Cycle-countingfrequenciesbased on the minimization of the sum of cycle-counting cost and penalty cost would give better stratified cycle-counting procedures. Cycle counting would periodically reset miscount errors to zero and adjust inventory records to tally with the actual physical counts. Once the proposed internal audit procedures and revised cycle-countingfrequenciesare implemented, the value of error rate K will go down over time. A lower value of K would further lower cycle-counting frequencies.

9.

IMPLEMENTATION OF EDI COMMUNICATION NETWORK WITH SUPPLIERS^

This section describes how EDI networks lower both ordering costs and lead times and consequently result in smaller lot sizes and smaller safety stocks.

42

9.1

Parts Management Models and Applications

EDI and JIT

Electronic Data Interchange (EDI) has been the new technological mode through which buyers and suppliers exchange relevant business information. Replenishing inventory through EDI networks help companies achieve substantial reductions in both ordering costs and lead times. It is a significant valid step in achieving Just-m-Time (JIT) inventory control. "JIT" is often perceived as switching to smaller lot sizes. Any change in lot sizes from their original optimal values that are not achieved through genuine parameter changes would impose penalties instead of achieving any economies The reduction in lot sizes should be achieved by changing necessary parameters. Lowering ordering cost and or lead time will reduce optimal lot sizes and safety stocks respectively. Reducing lot sizes without genuine parameter changes will do more damage than good. The simple model given below compares the effects of reducing lot sizes with and without parameter changes. We initially consider a singleitem inventory system with random demand and random lead time. The following notations are used in the model: i = Inventory holding rate/dollar/ year V = Unit cost of the item Q^= Fixed order quantity or replenishment lot size D^a = Average annual demand rate of the item D^Average daily demand rate of the item A= Fixed ordering cost per order Var(D)=Variance of daily demand rate Lj=Procurement lead time of the item L = Average lead time of the item Var(L)=Variance of the lead time of the item K= Safety stock factor

The total expected annual cost, T, is divided into two components, Ti and T2. The component Ti, represents the average annual cycle inventory holding and ordering cost. The component T2 represents the sum of the average annual safety stock holding cost (T2') and the annual stockout cost

Introduction to Parts Management

43

The average annual cycle holding and ordering cost, Ti (Q), is given by Ti(Q) = iv(Q/2) + ( 5 . / Q ) A Minimization of this cost yields optimal lot size as

Q*= ^llADahvi The optimal value of Ti(Q) is given by Ti(Q*) = (iv/2) -jlADaliv

+ (Da/^2ADa/iv)

A

I.e.,

T,{Q^)=^2ADaliv

(1)

Suppose that we change the lot size from Q* to Q=KQ*, where K< 1. Then Ti/(Q) is given by Ti (KQ*) = (ivK/2) ^llADaliv

-^(Da /{K^jlADa

I iv)) A

I.e.

Ti (KQ*)= ((K^+1)/2K) ^2ADa/iv since ( ( K V I ) / 2 K ) > 1 for all K.

> ^lADaiv

,

(2)

44

Parts Management Models and Applications Hence, any reduction in Q* imposes a penalty.

T,(KQn

^t(cr

Ti'(Q*')

KQ*

Q*

Q*

Figure 2-13. Graph of T, (KQ*) for Values of K 0

(7)

Optimal Division of Items

67

For the values of the parameters in the study, condition (7) holds for all classes. Since the values of partial derivatives of (f) (ij) with respect to Dj and Cj change sign once only, the regions Si and S2 are contiguous. In Table 3-3 items above the cut form set Si, and those below the cut form set S2

7.

CONCLUSION

The current division of the set S in the company follows an itembased approach from the dealers' point of view. The items which dealers decide to stock have to be individually profitable to them. They usually compare holding cost against special delivery cost in making these decisions. The customer's delay cost is usually ignored in their consideration. Table 2-4. Divisions of Set S into Si and S2 along with Captured Market Share and Profitability for the Three Cases.

Company Item-based Approach

Dealers Item-based Approach

Systems Approach

6,482 3,017 79,770,401 72,582,397

6,262 3,237 79,770,401 70,959,780

5,872 3,627 79,770,401 72,926,904

Pi= Profit from company's direct sales

118,542

255,759

117,694

P2= Profit from dealer items

886,078

712,018

891,946

P= Total profit

1,004,620

967,777

1,009,640

Performance Parameters Number of items in sets Si S2

Potential sales Captured sales

Table 3-4 shows results for the case study. The systems approach as compared to the company item-based approach results in a switch of 610 items from set Si to S2, with an additional sale of $344,507, and when compared to dealer item-based approach, a switch of 390 items with an

68

Parts Management Models and Applications

additional sale of $1,967,124 occurs. These comparisons are shown in Table 3-4. The optimal value of the parameters for the two lines used in the system's approach are: i=\, i^ =90, i2= 40. The impact of price has been ignored because various companies operate under the policy of match the competitors' prices. If a company were not operating under this policy then certainly price levels would influence captured demand. A dealer item-based approach is the one that is most commonly prevalent in the service parts distribution sector. Most car dealerships' service centers will fall in this category. For most of the unscheduled nonmaintenance repairs a customer has to make more than one visit for repairs. In a competitive environment, a system-based approach is definitely more desirable. Dealers' item-based approach is myopic. It ignores customers' delay cost. A company item-based approach does include the customers' delay cost. It may be acceptable in a non-competitive market environment. However, in a competitive environment, a system-based approach is definitely a more desirable one to follow.

1

Adapted from the paper by authors: Kumar, Sameer and Arora, Sant, (1990),"Customer Service Effect in Parts Distribution System Design", International Journal of Physical Distribution and Logistics Management, Vol. 20, No. 2, pp. 31-39.

Chapter 4 OPTIMAL ORDERING PROCEDURES FOR A MULTI-ITEM COMMON SUPPLIER SYSTEM

This chapter presents two models for a multi-item common supplier system with constant and random demand rates respectively for various items. In the first model, optimal inventory-management rules are developed allowing for planned stockouts, whose optimal values are determined on the basis of the total cost minimization. The second model is structured on new heuristics ordering rules for managing multi-items. In this model, the inventory position for each item is continuously reviewed and an order is placed when the projected stockout cost for all items exceeds a certain multiple of the average ordering cost. Rules are offered for determining which items to include in the order, and also for determining order-up-to-level for each item. These rules involve two parameters, whose optimal values are estimated by simulation.

1.

CONSTANT DEMAND FOR VARIOUS ITEMS^

In this section, we review theoretical basis for the first model and illustrate the application of the model (including cost evaluation and comments on its performance) using an existing example in the literature and finally provide some concluding remarks on the model.

70

Parts Management Models and Applications

1.1

The Model - Constant Demand Model

Inventory problem for multi-item system with a common vendor is considered. The ordering cost is assumed to have two components: a major common ordering cost S is incurred whenever an order is placed, and a minor ordering cost Sj is incurred if item j is included in the order. The demand for item j is assumed to be at a constant rate Dj. This problem has been considered in the literature with stockout costs being infinity (Goyal 1974). In our formulation, the stockout costs are finite, with the result that there are planned stockouts at the end of the ordering cycle for each item. The values of stockout cost may be difficult to assign directly. An inventory or production manager can make a choice more easily among different alternatives with varying stockout levels when their associated holding-cost components are made available to him. The value for stockout cost bj for item j is assigned once his choice is known (assuming that the manager's choice is the optimal one). In our formulation, the stockout levels are determined as a result of the optimization process instead of being prescribed externally. The following notations are used in the proposed model: Notations * is used as a superscript to denote the optimal value for a variable. n = number of items N = number of purchase orders in a planning period Nj = number of replenishments for the jth item in the planning period kj = relative ordering frequency for the jth item (equal to N/Nj) Uj = fraction of the supply available immediately after replenishment and meeting the back-orders for item j S = common ordering cost per order, which is independent of the number of items included in the order and the size of orders for these items Sj = minor part of the ordering cost incurred whenever item; is included in the order Dj = deterministic demand rate for item j T = common inter-order time hj = holding cost per unit per unit period for item j bj = stockout cost per unit per unit period for item j C = total variable system cost for the planning period; this includes ordering cost, holding cost and stockout cost

Optimal Ordering Procedures

71

The following additional assumptions are made here: (i) The procurement lead time is constant for all items. (ii) Minimization of total cost per unit period is taken as the criterion of optimality. (iii) The parameters of the system have constant values over time. The total variable cost for all items in the planning period will be

Substituting Nj = N/ kj = l/( kj T) in (1), we get C(N,{Nj},{Uj}=C(T,{kj},{Uj})

= ( S + ^ SA)/T+(^ Yj^^hU]^\

E Djbjkj(l-Uj)^))T.

(2)

T, {Uj} are continuous variables, whilst {kj}are non-negative integers. Figure 4-1 shows the relationship between these three sets of variables.

Parts Management Models and Applications

72

\, o

'fN v.

^ ^ \

T~r

1 Time

•la

N * Figure 4-1. Illustration of inventory on-hand graph over time for two items, one with kj = 1, and the other with kj = 3.(

On-hand inventory for item 1)(

On-hand

inventory for item 2)

Substituting A= S + ^

S/kj and

7=1

^

7=1

^

7=1

we have C(T, {kj}, {Uj})=A/T+BT. Optimizing with respect to T, we have

I*=4ATB and C{T*) = A^A/B

(3) (4)

+ BylA/B =

lyfls.

(5)

Optimal Ordering Procedures

73

We now optimize total cost function C with respect to {Uj}. Minimizing Q}, which is equivalent to minimizing C, we get f/;=Zj^/(6^+/j^)forj = l , 2 ,

n.

(6)

Substituting the optimal values for T* and {U^} in the total cost equation (2), we get

C(T*, {Uj}, {kj})=

l\\S^•YS^ /A:,]J[lX^,^^y(^ H^ +^))' +^Z^y^^;(^ '^^ +^))'] "•^ ^ - i J

7=1

J

J

J ^ J

^ J

J '^

^

V ^v=i

L ^

^y=i

Optimal values for {kj} are obtained w hen the following conditions are satisfied: C(T*,{^;}, k\,{k]^+m))


a/CS + ^S/k^) j=i

(17).

j=i

j=i

j=i

where aj = aj'(2/L) In computing the total stockout cost it has been assumed that at the time of placing an order at most one order is pending. With this assumption, just prior to placing an order, inventory position would equal inventory on hand. 4.4.6

Which items to include in the order

An item is included in an order if its expected stockout cost over the sum of the lead time and the average order cycle time exceeds or equals a constant multiple a2 of the item's ordering cost. That is, include item j in the order, if, bj(L/2)VL + T*ajG,((Ij(t) - (L + T * ) D J ) / V L +1*0^) > a^'S^

b j V L 7 r ' a j G , ( ( I j ( t ) - (L + T*)Dp/A/L + T*aj) > a^S^,

(19)

(20)

where Q.^ = ^^Q.I\J) 4.4.7 How much to order for items being ordered The rule for the order quantity for item j is given by qj = Wj - I j ( t ) = D^kjT* +p(b^/h.)VLa^ -I^(t) (21) Implicit within our inventory operational management rules are parameters ai, a2 and (3. A proper choice of ai, a2 and p values will lead to an efficient

88

Parts Management Models and Applications

distribution of the incremental cost due to demand randomness among ordering, inventory holding and stock-out cost components. Approximate optimal values of ai, a2 and P are obtained employing simulation. In the next section, a small example is described to illustrate how these heuristic rules are more realistic as compared to existing approaches available in the literature.

5.

EXAMPLE

In this section, we illustrate and compare our ordering rules (where an order is placed when the total expected stock-out cost over the lead time exceed a multiple of the total ordering cost) with Love's ordering rules (where an order is placed when inventory position of the first item hits its re-order level Sj) using his four items example through Monte-Carlo simulation. The problem data are identical for the two ordering rules, excepting we have assumed certain values of bj's, whereas we do not know the values for bj's assumed by Love in his example. The simulation covered a period of 190 days. In order to minimize the impact of differences due to initial conditions, the first 10 days were not included in the performance statistics. The data are given in Table 4-4. The starting inventory for item j , for both models was selected equal to sum of the average demand over kjT* plus the safety stock. The simulation was carried out following ordering rules of two methods. The search for the optimal values of parameters a and p was made using the sequential grid technique. Table 4-5 gives performance statistics such as, total number of orders placed in the simulation period, order cost per unit period, holding cost per unit period, stockout cost per unit period and total variable cost per unit period for various values of a and p around the optimal value.

Optimal Ordering Procedures

89

Table 4-4. Data for a four items common vendor example

n=4, S=400, L=l

J

Dj

1

4

2

hj

b.

Sj

2

2

3

2

9

3

4

2

1

3

4

2

6

1.5

3

4

16

4

5

2.5

5

J

V

J

Table 4-5. Grid showing sequential search of minimum total cost per unit period = $241.70 by our heuristic model

2

1

0.5

M= 19 Cl= 43.38 C2= 75.00 C3= 249.61 C = 367.99 M= 27 Cl= 61.65 C2= 98.00 C3= 90.29 C= 249.94 M= 36 Cl= 82.20 C2= 136.00 C3= 35.12 C= 253.32

M= 20 01=45.67 02= 68.00 03=239.15 0= 352.82 M= 27 01= 61.65 02= 93.00 03= 87.05 0=241.70 M= 35 01=82.20 02= 125.00 03= 37.87 0= 245.07

M= 20 01=45.67 02=68.00 03=241.64 0=355.31 M= 28 01= 63.93 02= 89.00 03= 91.15 0= 244.08 M= 37 01= 84.48 02=118.00 03= 42.40 0= 249.88

a

1.0

0.5

0.2

90

Parts Management Models and Applications

Our matching solution with Love's solution (in terms of equal stockout cost) when a==0.02 and p=l is given in Table 4-6. The details of performance statistics for our non-optimal solution are given in Table 4-11. Table 4-6. Value of a and p, sequentially searched by grid method and refining the grid until stockout cost per unit period in our heuristic model matched with Love's model

p

2

1

0.5

M = 38 Cl= 86.73 C2= 284.00 C3= 12.55 C= 383.28 M = 39 Cl= 89.03 C2= 296.00 C3= 11.57 C= 396.60 M = 39 Cl= 91.23 C2= 295.00 C3= 9.06 C= 395.38

M = 38 €1= 86.76 C2= 260.00 C3= 13.95 C= 360.71 M= 40 Cl= 91.33 €2= 265.00 C3= 11.46 C= 367.79 M= 42 Cl= 95.90 C2= 287.00 C3= 8.88 C= 391.78

M= 39 Cl= 89.05 C2= 245.00 C3= 12.65 C= 346.70 M= 42 Cl= 95.90 €2= 265.00 €3= 10.27 C=361.17 M= 43 Cl= 98.18 C2= 271.00 C3= 9.93 C= 379.11

a

0.03

0.02

0.01

Figures 4-2 through 4-5, display response surfaces plots for ordering cost, holding cost, stockout cost and total cost per unit period respectively for various values of a and (3 parameters. These graphs use results reported in Table 4-5, which are based on the heuristic model proposed in this chapter.

Optimal Ordering Procedures

91

100 Ordering Cost per unit period

80 gQ 40 20 0

Alpha

0 22

Beta

Figure 4-2. Graph illustrating Ordering Cost per unit period for various values of parameters - Alpha(a) and Beta(P).

Holding Cost per unit period

Alpha

Figure 4-3. Graph illustrating Ordering Cost per unit period for various values of parameters - Alpha(a) and Beta(P).

92

Parts Management Models and Applications 250 o* .. * 200 Stockout Cost per 150 unit period

100 50 0

Beta

Figure 4-4. Graph illustrating Stockout Cost per unit period for various values of parameters - Alpha(a) and Beta(P).

400 -r . . ^ -^ 300 Total Cost per unit 200 period ^ 100

Alpha

0-5 ^ ^ 0 2;

Beta

Figure 4-5. Graph illustrating Total Cost per unit period for various values of parameter Alpha(a) and Beta(P). Table 4-7 gives values of parameters for Love's static model. Table 4-8 gives performance statistics for the random case following his ordering rules.

Optimal Ordering Procedures

93

Table 4-7. Operational Management Parameters for Love's Static Model a=3,95 Item

Starting

Safety

inventory at t=0

included in Wj

stock

Cj

Wj

Sj

1

15

9

17

12

20

2

25

5

31

21

45

3

14

2

18

12

28

4

79

6

51

32

112

Table 4-8. Simulation Performance Statistics following Love's Heuristic model

Number of orders placed = 94 Item

Average inventory

Stockout

Unit days short

Orders for items

frequencies 7

55

55

68

14

58

58

69

3

11

20

20

55

4

42

28

28

41

1 2

Total simulation days used

=180

Order cost per unit period

=216.54

Holding cost per unit period

=349.00

Stockout cost per unit period

= 11.24

Total variable cost per unit period

=576.78

Table 4-9 gives values of parameters for our static model. Tables 4-10 and 4-11 give performance statistics following our ordering rules.

94

Parts Management Models and Applications Table 4-9. Static Model based operational management parameters for the heuristic model in this chapter {Ry = (hjDj/Sj).(bj/(bj +hj))}

a=0.001, p=8.5,r=4.271 Starting Item

inventory at t=0

1

26

2 3 4

-

Safety stock

Wj

included in Wj

bj/(bj+l^)

kjo

Rj'

kji

9

27

3/5

8/5

1

1

43

5

43

1/3

12/5

1

1

19

2

19

1/5

16/3

1

1

74

6

75

1/3

12

1

1

Table 4-10 gives performance statistics when the total cost per unit period is minimum. Our total cost is 58% lower than Love's total cost. With the given data, according to the optimal solution calculated by our method, the stockout level is higher than the stockout level in Love's solution. If a better service level is desired in terms of reduced stockout then the right method to achieve it will be found by assigning higher values to parameter's bj's. However, since we do not know Love's bj's, we assume his stockout level as being prescribed by management.

optimal Ordering Procedures

95

Table 4-10. Simulation Performance Statistics for the optimal solution using heuristic model proposed in this chapter KufiTib*! of orckrs placed = ll Item

Avctragf

Stock-