INVENTORY CONTROL Second Edition Recent titles in the INTERNATIONAL SERIES IN OPERATIONS RESEARCH & MANAGEMENT SCIENCE Frederick S. Hillier, Series Editor, Stanford University Maros/ COMPUTATIONAL TECHNIQUES OF THE SIMPLEX METHOD Harrison, Lee & Neale/ THE PRACTICE OF SUPPLY CHAIN MANAGEMENT: Where Theory and Application Converge Shanthikumar, Yao & Zijm/ STOCHASTIC MODELING AND OPTIMIZATION OF MANUFACTURING SYSTEMS AND SUPPLY CHAINS Nabrzyski, Schopf & W^glarz/ GRID RESOURCE MANAGEMENT: State of the Art and Future Trends Thissen & Herder/ CRfTICAL INFRASTRUCTURES: State of the Art in Research and Application Carlsson, Fedrizzi, & Fuller/ FUZZY LOGIC IN MANAGEMENT Soyer, Mazzuchi & Singpurwalla/ MATHEMATICAL RELIABILITY: An Expository Perspective Chakravarty & Eliashberg/ MANAGING BUSINESS INTERFACES: Marketing, Engineering, and Manufacturing Perspectives Talluri & van Ryzin/ THE THEORY AND PRACTICE OF REVENUE MANAGEMENT Kavadias & Loch/PROJECT SELECTION UNDER UNCERTAINTY: Dynamically Allocating Resources to Maximize Value Brandeau, Sainfort & Pierskalla/ OPERATIONS RESEARCH AND HEALTH CARE: A Handbook of Methods and Applications Cooper, Seiford & Zhu/ HANDBOOK OF DATA ENVELOPMENT ANALYSIS: Models and Methods Luenberger/ LINEAR AND NONLINEAR PROGRAMMING, 2"'' Ed Sherbrooke/ OPTIMAL INVENTORY MODELING OF SYSTEMS: Multi-Echelon Techniques, Second Edition Chu, Leung, Hui & Cheung/ 4th PARTY CYBER LOGISTICS FOR AIR CARGO Simchi-Levi, Wu & Shen/ HANDBOOK OF QUANTITATIVE SUPPLY CHAIN ANALYSIS: Modeling in the E-Business Era Gass & Assad/ AN ANNOTATED TIMELINE OF OPERATIONS RESEARCH: An Informal History Greenberg/ TUTORIALS ON EMERGING METHODOLOGIES AND APPLICATIONS IN OPERATIONS RESEARCH Weber/ UNCERTAINTY IN THE ELECTRIC POWER INDUSTRY: Methods and Models for Decision Support Figueira, Greco & Ehrgott/ MULTIPLE CRITERIA DECISION ANALYSIS: State of the Art Surveys Reveliotis/ REAL-TIME MANAGEMENT OF RESOURCE ALLOCATIONS SYSTEMS: A Discrete Event Systems Approach Kail & Mayer/ STOCHASTIC LINEAR PROGRAMMING: Models, Theory, and Computation Sethi, Yan & Zhang/ INVENTORY AND SUPPLY CHAIN MANAGEMENT WITH FORECAST UPDATES Cox/ QUANTITATIVE HEALTH RISK ANALYSIS METHODS: Modeling the Human Health Impacts of Antibiotics Used in Food Animals Ching & Ng/ MARKOV CHAINS: Models, Algorithms and Applications Li & Sun/NONLINEAR INTEGER PROGRAMMING Kaliszewski/ SOFT COMPUTING FOR COMPLEX MULTIPLE CRITERIA DECISION MAKING Bouyssou et al/ EVALUATION AND DECISION MODELS WITH MULTIPLE CRITERIA: Stepping stones for the analyst Blecker & Friedrich/ MASS CUSTOMIZATION: Challenges and Solutions Appa, Pitsoulis & Williams/ HANDBOOK ON MODELLING FOR DISCRETE OPTIMIZATION Herrmann/ HANDBOOK OF PRODUCTION SCHEDULING * A list of the early publications in the series is at the end of the book * INVENTORY CONTROL Second Edition Sven Axsater ^ Spriinger Sven Axsater Lund University Lund, Sweden Library of Congress Control Number: 2006922871 ISBN-10: 0-387-33250-2 (HB) ISBN-10: 0-387-33331-2 (e-book) ISBN-13: 978-0387-33250-5 (HB) ISBN-13: 978-0387-33331-1 (e-book) Printed on acid-free paper. © 2006 by Springer Science+Business Media, LLC 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, LLC, 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 know or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if the 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.com About the Author Sven Axsater is Professor of Production Management at Lund University since 1993. He is also head of the Department of Industrial Management and Logistics.
Before coming to Lund he held professorships at Linkoping Insti- tute of Technology and Lulea University of Technology. He served as Visit- ing Professor at North Carolina State University in 1980 and at Hong Kong University of Science and Technology in 2001. The main focus of Sven Axsater's research has been production and in- ventory control. Past and current interests include: hierarchical production planning, lot sizing, and most recently multi-echelon inventory systems.
He has published numerous papers in the leading journals in his research area, and has taught various courses on production and inventory control at uni- versities in different parts of the world. Sven Axsater has also served in an editorial capacity in various journals, including many years of service as As- sociate Editor of both Operations Research and Management Science. Sven Axsater has been President of the International Society of Inventory Research, and Vice President of the Production and Operations Management Society. He is also a member of the Royal Swedish Academy of Engineering Sciences.
In 2005 he was awarded the Harold Lamder Memorial Prize by the Canadian Operational Research Society for distinguished international achievement in Operational Research. In addition, he has a vast consulting experience in the inventory man- agement area. He has implemented inventory control in several companies, and has also developed software for commercial inventory control systems. CONTENTS Preface xv 1 INTRODUCTION 1 1.1 Importance and objectives of inventory control 1 1.2 Overview and purpose of the book 2 1.3 Framework 5 References 5 2 FORECASTING/ 2.1 Objectives and approaches 7 2.3 Trend-seasonal model 10 2.4 Choosing demand model 10 2.2 Comparing exponential smoothing to a moving average 13 2.3 Practical considerations and an example 14 2.5 Exponential smoothing with trend 16 2.2 Practical considerations and an example 17 2.6 Winters' trend-seasonal method 18 2.2 Practical considerations and an example 20 2.7 Using regression analysis 21 2.7 Forecasting demand for a trend model 21 2.2 Practical considerations and an example 23 2.3 Forecasts based on other factors 24 2.4 More general regression models 25 2.8 Sporadic demand 26 INVENTORY CONTROL 2.9 Box-Jenkins techniques 27 2.1 Common error measures 29 2.2 Updating MAD or a^ 30 2.3 Determining the standard deviation as a function of demand 32 2.4 Forecast errors for otfier time periods 32 2.5 Sales data instead of demand data 34 2.2 Checf<ing that the forecast represents the mean 35 2.12 fVlanual forecasts 36 References 37 Problems 38 3 COSTS AND CONCEPTS 43 3.1 Considered costs and other assumptions 44 3.2 Ordering or setup costs 44 3.3 Shortage costs or service constraints 45 3.4 Other costs and assumptions 45 3.2 Different ordering systems 46 3.2 Continuous or periodic review 47 3.3 Different ordering policies 48 3.2 (^, 5) policy 49 References 50 4 SINGLE-ECHELON SYSTEMS: DETERMINISTIC LOT SIZING 51 4.1 The classical economic order quantity model 52 4.1 Optimal order quantity 52 4.2 Finite production rate 55 4.5 Time-varying demand 61 4.6 The Wagner-Whitin algorithm 63 CONTENTS ix 4.7 The Silver-Meal heuristic 66 4.8 A heuristic that balances holding and ordering costs 68 4.9 Exact or approximate solution 70 References 70 Problems 72 5 SINGLE-ECHELON SYSTEMS: REORDER POINTS 77 5.1 Discrete stochastic demand 77 5.1 Compound Poisson demand 77 5.2 Logarithmic compounding distribution 80 5.3 Geometric compounding distribution 82 5.5 Fitting discrete demand distributions in practice 85 5.2 Continuous stochastic demand 85 5.1 Normaily distributed demand 85 5.2 Gamma distributed demand 86 5.3 Continuous review (R, Q) policy - inventory level distribution 88 5.1 Distribution of ttie inventory position 88 5.2 An important reiationsliip 90 5.3 Compound Poisson demand 90 5.4 Normally distributed demand 91 5.6 Determining the safety stock for given Si 96 5.7 Fill rate and ready rate constraints 97 5.1 Compound Poisson demand 97 5.2 Normally distributed demand 98 5.8 Fill rate - a different approach 99 5.9 Shortage cost per unit and time unit 101 5.1 Compound Poisson demand 101 5.2 Normally distributed demand 103 5.10 Shortage cost per unit 106 5.11 Continuous review (s, S) policy 107 5.12 Periodic review - fill rate 109 5.2 Compound Poisson demand - (R, Q) policy 111 5.3 Compound Poisson demand - (s, S) policy 112 5.4 Normally distributed demand - (R, Q) policy 113 5.13 The newsboy model 114 5.14 A model with lost sales 117 INVENTORY CONTROL 5.15 Stochastic lead-times 119 5.1 Two types of stochastic lead-times 119 5.2 Handling sequential deliveries independent of the lead-time demand 120 5.3 Handling independent lead-times 122 5.4 Comparison of the two types of stochastic lead-times 123 References 124 Problems 126 6 SINGLE-ECHELON SYSTEMS: INTEGRATION - OPTIMALITY 129 6.1 Joint optimization of order quantity and reorder point 129 6.2 An iterative technique 133 6.3 Fill rate constraint - a simple approach 135 6.2 Optimality of ordering policies 137 6.
Optimality of(R, Q) policies when ordering in batches 138 6.2 Optimality of (s,S) policies 140 6.3 Updating order quantities and reorder points in practice 140 References 145 Problems 146 7 COORDINATED ORDERING 149 7.1 Powers-of-two policies 150 7.1 The Economic Lot Scheduling Problem (ELSP) 155 7.2 The independent solution 156 7.3 Common cycle time 157 7.6 Other problem formulations 163 7.2 Time-varying demand 163 7.1 A generalization of the classical dynamic lot size problem 163 7.2 Application of mathematical programming approaches 170 7.3 Production smoothing and batch quantities 170 CONTENTS 7. An iterative technique 174 7. Roundy's 98 percent approximation 176 7.2 A stochastic model 180 References 181 Problems 183 8 MULTI-ECHELON SYSTEMS: STRUCTURES AND ORDERING POLICIES 187 8.1 Inventory systems in distribution and production 188 8.1 Distribution inventory systems 188 8.2 Production inventory systems 189 8.4 Lateral transshipments in inventory systems 192 8.5 Inventory models with remanufacturing 194 8.2 Different ordering systems 195 8.1 Installation stock reorder point policies and KAN BAN policies 196 8.2 Echelon stock reorder point policies 197 8.3 Comparison of installation stock and echelon stock policies 198 8.4 Material Requirements Planning 204 8.5 Ordering system dynamics 213 References 215 Problems 217 9 MULTI-ECHELON SYSTEMS: LOT SIZING 221 9.1 Identical order quantities 222 9.1 Infinite production rates 222 9.2 Finite production rates 223 9.1 A simple serial system with constant demand 225 9.2 Roundy's 98 percent approximation 230 INVENTORY CONTROL 9.3 Time-varying demand 236 9.1 Sequential lot sizing 236 9.2 Sequential lot sizing with modified parameters 238 9.4 Concluding remarks 241 References 242 Problems 243 10 MULTI-ECHELON SYSTEMS: REORDER POINTS 247 10.1 The Clark-Scarf model 248 10.2 The Clark-Scarf approach for a distribution system 256 10.2 The METRIC approach for distribution systems 261 10.3 Two exact techniques 266 10.1 Disaggregation of warehouse backorders 266 10.4 Optimization of ordering policies 271 10.5 Batch-ordering policies 273 10.1 Some basic results 277 10.2 METRIC type approximations 278 10.3 Disaggregation of warehouse backorders 279 10.4 Following supply units through the system 280 10.1 Guaranteed service model approach 281 10.2 Coordination and contracts 283 10.1 The newsboy problem with two firms 284 10.2 Wholesale-price contract 285 10.3 Buyback contract 286 References 287 Problems 291 11 IMPLEMENTATION 295 11.1 Preconditions for inventory control 295 11.1 Updating inventory records 296 11.2 Auditing and correcting inventory records 297 11.2 Performance evaluation 298 CONTENTS xiii 11.2 Development and adjustments 299 11.1 Determine the needs 300 11.2 Selective inventory control 301 11.3 Model and reality 302 11.4 Step-by-step implementation 303 11.6 Short-run consequences of adjustments 305 11.7 Education 306 References 307 APPENDIX 1 ANSWERS AND HINTS TO PROBLEMS 309 APPENDIX 2 NORMAL DISTRIBUTION TABLES 321 INDEX 325 Preface Modem information technology has created new possibihties for more so- phisticated and efficient control of supply chains. Most organizations can re- duce their costs associated with the flow of materials substantially.
Inventory control techniques are very important components in this development proc- ess. A thorough understanding of relevant inventory models is a prerequisite for successful implementation. I hope that this book will be a useful tool in acquiring such an understanding. The book is primarily intended as a course textbook.
It assumes that the reader has a good basic knowledge of mathematics and probability theory, and is therefore most suitable for industrial engineering and management science/operations research students. The book can be used both in under- graduate and more advanced graduate courses. About fifteen years ago I wrote a Swedish book on inventory control. This book is still used in courses in production and inventory control at sev- eral Swedish engineering schools and has also been appreciated by many practitioners in the field.
Positive reactions from many readers made me contemplate writing a new book in English on the same subject.