SUPPLY CHAIN GAMES: OPERATIONS MANAGEMENT AND RISK VALUATION Recent titles in the INTERNATIONAL SERIES IN OPERATIONS RESEARCH & MANAGEMENT SCIENCE Frederick S. Hillier, Series Editor, Stanford University 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 Axsäter/ INVENTORY CONTROL, 2 nd Ed. Hall/ PATIENT FLOW: Reducing Delay in Healthcare Delivery Józefowska & Wglarz/ PERSPECTIVES IN MODERN PROJECT SCHEDULING Tian & Zhang/ VACATION QUEUEING MODELS: Theory and Applications Yan, Yin & Zhang/ STOCHASTIC PROCESSES, OPTIMIZATION, AND CONTROL THEORY APPLICATIONS IN FINANCIAL ENGINEERING, QUEUEING NETWORKS, AND MANUFACTURING SYSTEMS Saaty & Vargas/ DECISION MAKING WITH THE ANALYTIC NETWORK PROCESS: Economic, Political, Social & Technological Applications w. Benefits, Opportunities, Costs & Risks Yu/ TECHNOLOGY PORTFOLIO PLANNING AND MANAGEMENT: Practical Concepts and Tools Kandiller/ PRINCIPLES OF MATHEMATICS IN OPERATIONS RESEARCH Lee & Lee/ BUILDING SUPPLY CHAIN EXCELLENCE IN EMERGING ECONOMIES Weintraub/ MANAGEMENT OF NATURAL RESOURCES: A Handbook of Operations Research Models, Algorithms, and Implementations Hooker/ INTEGRATED METHODS FOR OPTIMIZATION Dawande et al/ THROUGHPUT OPTIMIZATION IN ROBOTIC CELLS Friesz/ NETWORK SCIENCE, NONLINEAR SCIENCE and INFRASTRUCTURE SYSTEMS Cai, Sha & Wong/ TIME-VARYING NETWORK OPTIMIZATION Mamon & Elliott/ HIDDEN MARKOV MODELS IN FINANCE del Castillo/ PROCESS OPTIMIZATION: A Statistical Approach Józefowska/JUST-IN-TIME SCHEDULING: Models & Algorithms for Computer & Manufacturing Systems Yu, Wang & Lai/ FOREIGN-EXCHANGE-RATE FORECASTING WITH ARTIFICIAL NEURAL NETWORKS Beyer et al/ MARKOVIAN DEMAND INVENTORY MODELS Shi & Olafsson/ NESTED PARTITIONS OPTIMIZATION: Methodology And Applications Samaniego/ SYSTEM SIGNATURES AND THEIR APPLICATIONS IN ENGINEERING RELIABILITY Kleijnen/ DESIGN AND ANALYSIS OF SIMULATION EXPERIMENTS Førsund/ HYDROPOWER ECONOMICS * A list of the early publications in the series is at the end of the book * SUPPLY CHAIN GAMES: OPERATIONS MANAGEMENT AND RISK VALUATION Konstantin Kogan Bar-Ilan University, Israel Charles S. Tapiero Polytechnic University of New York, US and ESSEC, France Konstantin Kogan Charles S. Tapiero Bar-Ilan University Polytechnic University of NY, USA Israel and ESSEC, France Series Editor: Fred Hillier Stanford University Stanford, CA, USA Printed on acid-free paper. © 2007 Springer Science+Business Media, LLC 9 8 7 6 5 4 3 2 1 springer.com 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 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. Library of Congress Control Number: 2007929861 e-ISBN 978-0-387-72776-9 ISBN 978-0-387-72775-2 For Kathy and Carole For their continuous care and support Operations and industrial modeling and management have a long history dating back to the first Industrial Revolution. Scheduling, inventory con- trol, production planning, projects management, control charts, statistical records, customer satisfaction questionnaires, rankings and benchmarking. are some of the tools used for the purpose of better managing operations and services. The complexity of operations and logistics problems have increased, however, with the growth of supply chains, rendering traditional operational and risk management issues far more complex and strategic- game-like at the same time. Similarly, we have gained increased experi- ence in defining, measuring, valuing and managing risks that result from the particular environment that supply chains create. Increasingly, there is a felt need for convergence between the traditional tooling of industrial- logistics and the economic realities of supply chains operating on a global scale. This book provides students in logistics, risk engineering and econo- mics as well as business school graduates the means to model and analyze some of the outstanding issues currently faced in managing supply chains. The growth and realignment of corporate entities into strategic supply chains, global and market sensitive, are altering the conception of operations modeling. Now far more strategic and sensitive to external events and to their externalities, they require new avenues of research. There is a need to rethink and retool traditional approaches to operations logistics and tech- nology management so that these activities will be far more in tune with an era of global, cross-national supply chains. Today, supply chains are an essential ingredient in the quest for corporate survival and growth. Operations strategy in supply chains have mutated, however, assuming ever-expanding and strategic dimensions and augmenting appreciably the operational complexity and risks that modern enterprises face when they operate in an interdependent supply chain environment. These operational facets imply a brand new set of operational problems and risks that have not always been understood or managed. Supply chain managers have thus an important role to assume by focusing attention on PREFACE these operations and risks and in educating corporate managers about what these operation problems and their risks imply. Our purpose in this book will be to consider these problems in depth and to draw essential conclusions regarding their management in supply chains. For example, traditional operational problems (such as inventory control, quality management and their like) are expressed in a strategic and intertem- poral manner that recognizes the complexity and the interdependency of firms in a supply chain environment. Examples that highlight our concerns and how to deal technically with these problems will be extensively used. The book is directed necessarily towards advanced undergraduate stu- dents but will be made accessible to students, including those in operations engineering, who have a basic understanding of mathematical tools such as optimization, differential equations and some elements of game theory. When necessary, the book will utilize appendices to review basic mathematical tools, emphasizing their application rather than the theoretical underpin- nings. Similarly, a number of computer programs will be used for calcula- tions, bridging the gap between theory and practice. The book consists of three areas, each intimately dependent on one an- other, each emphasizing important facets of supply chains management operations. These include: • Supply Chains and Operations Modeling and Management • Intertemporal Supply Chains Management • Risk and Supply Chain Management The first area provides both traditional static and discrete-time models and their gradual extension to a supply chain environment, highlighting the new concerns of the supply chain environment. In addition, it emphasizes both one- and two-period problems while in the second area, we address essentially inter-temporal problems as differential games. The differential games are presented as natural continuous-time extensions of the corres- ponding static models so that the effect of various types of dynamics on supply chains may be assessed and insights gained. The third area deals with risk and supply chains as well as with numerous applications to the man- agement of quality in a supply chain environment and in managing inter- dependent (both in substance and in decision-making) operations. In this sense, the book highlights and resolves some important problems that address directly the needs and the complexity of supply chain management in a tractable and strategic setting. viii PREFACE Preface Part I: Supply Chains and Operations Modeling and Management 1 Supply chain operations management 3 1.1 Supply chain operations: a metamorphosis 4 1.2 Motivations and organization 5 1.3 Supply chains: needs and risks 10 1.4 Supply chains and operations management 12 1.5 Supply chains and inventory management 16 1.6 Quality and supply chain management 23 1.7 Games and supply chain management 29 1.8 Risk and supply chain management 35 Appendix: essentials of game theory 43 References 47 2 Supply chain games: modeling in a static framework 51 2.1 Static games in supply chains 51 2.2 Production/pricing competition 57 2.2.1 The pricing game 57 2.2.2 The production game 69 2.3 Stocking competition with random demand 81 2.3.1 The stocking game 81 2.3.2 The outsourcing game 92 2.4 Inventory competition with risk sharing 102 2.4.1 The inventory game with a buyback option 102 2.4.2 The inventory game with a purchasing option 109 References 116 3 Supply chain games: modeling in a multi-period framework 119 3.1 Stocking game 119 3.1.1 The stocking game in a multi-period formulation 119 3.1.2 The two-period system-wide optimal solution 122 3.1.3 Game analysis 126 vii CONTENTS 3.2.1 The replenishment game in a multi-period formulation 139 3.2.2 Game analysis 143 3.2.3 Empirical results and numerical analysis 150 References 153 Part II: Intertemporal Supply Chain Management 4 Supply chain games: modeling in an intertemporal framework 159 4.1 Differential games in supply chains 159 4.2 Intertemporal production/pricing competition 163 4.2.1 The differential pricing game 163 4.2.2 The differential production game 179 4.3 Intertemporal inventory games 193 4.3.1 The differential inventory game with endogenous demand 194 4.3.2 The differential inventory game with exogenous demand 218 4.4 Intertemporal subcontracting competition 238 4.4.1 The production balancing game 4.4.2 The differential outsourcing game 257 4.5 Intertemporal co-investment in supply chains 277 4.5.1 The differential investment and labor game 277 4.5.2 Short-run and long-run cooperation 288 References 296 5 Supply chain games: modeling in an intertemporal framework with periodic review 299 5.1 Two-period inventory outsourcing 299 5.2 Game analysis 314 References 322 6 Sustainable collaboration in supply chains 323 6.1 Multi-echelon supply chains with uncertainty 323 6.2 Supply chains with limited resources 335 6.2.1 Production control of parallel producers with random demands for products 336 6.2.2 Production control of parallel producers with maintenance 354 6.3 Supply chains with random yield 363 References 373 3.2 Replenishment game: case studies 137 238 x CONTENTS 7 Risk and supply chains 377 7.1 Risk in supply chains 378 7.2 Risk practice in supply chains 383 7.3 Supply chain risks and money 386 7.4 Risk valuation 389 7.5 Selected cases and problems 403 7.6 Collaboration, risks and supply chains 412 References 424 8 Quality and supply chain management 431 8.1 Quality and contracts 433 8.2 Mutual sampling 436 8.2.1 The risk neutral game 438 8.2.2 Centralized control and collaboration 445 8.3 Yield and control 452 8.3.1 The supply quality and control game 454 8.3.2 Optimal yield 459 8.4 Risk in a collaborative supply chain 463 8.4.1 A Neymann-Pearson framework for risk control 463 8.4.2 Special cases and extensions 470 References 479 Appendix: optimality conditions in single- and two-player dynamic games 483 A1.1 Dynamic problems 483 A1.2 Dynamic programming 487 A1.3 Stochastic dynamic programming 493 A1.4 The maximum principle 496 A1.5 Non-cooperative dynamic games 500 References 506 Index 507 CONTENTS Part III: Risk and Supply Chain Management xi [...]...PART I SUPPLY CHAINS AND OPERATIONS MODELING AND MANAGEMENT 1 SUPPLY CHAIN OPERATIONS MANAGEMENT Operations and industrial modelling and management have a long history dating back to the first industrial revolution With the growth of supply chains, the complexity of operations and logistics problems has increased rendering traditional operational management issues far more complex and of increased... of supply chains Examples: The Many Faces of Supply Chains The common view of supply chains, as stated in Figures 1. 1, 1. 2 and 1. 3 involves supply chains with intra-firms operations focused on production and inventory management and on procurement and the management of logistics and distribution Often, some of these functions are outsourced as well, leading to considerable diffusion in a firm’s operations. .. Quality and Control OM Inventory Forecasting Scheduling Capacity Transportation Measurement Figure 1. 1 Operations Management Intra Firms Operations and Logistics In industrial and logistics management, supply chains have become the dominant organizational model, fed by and feeding the important changes in technology and operations management of the last half century In Figures 1. 1, 1. 2 and 1. 3, for... operations and educating corporate managers about what these operations imply, how to value them and to “internalize” them into the firm’s economic analyses so that the supply chain can be managed better 4 1 SUPPLY CHAIN OPERATIONS MANAGEMENT We begin in this chapter by an overview of the transformation of logistics and operations into a concern for the management of supply chains operations 1. 1 SUPPLY. .. ACCOR These supply chains arose as an alternative to centralized and vertical supply chains” where material, manufacturing and products management, logistics and distribution, wholesaling and retailing and marketing channels 10 1 SUPPLY CHAIN OPERATIONS MANAGEMENT are integrated as a whole and centrally designed and managed The vertically integrated chains are based on a collective of agents and firms... an average cost minimization: AC K c1QT / 2 , T T Q x yields Q* 2 xK / c1 and AC * Kx Q* c1Q* 2 2 xKc1 Thus, by a mis-specification (or weighted inventory cost, by k, we have: Q' 2 xK / kc1 , AC1 2 xKkc1 20 1 SUPPLY CHAIN OPERATIONS MANAGEMENT When we compare this to the centralized solution (k =1) , we obtain the following costs: AC1 AC k and therefore AC1 AC AC1 1 1 k In other words, the percentage... and communication technology Incentives management Technological, political and social constraints Re-scheduling, supply and products delay management and their penalties Transportation scheduling and logistic controls Service and product quality and their controls Customer prioritization, upstream and downstream 16 1 SUPPLY CHAIN OPERATIONS MANAGEMENT The integration of aggregate operations into supply. .. Positioning” (19 84) Hayes and Wheelright presented a number of considerations spanning demand volatility and the interaction effects of delays and uncertainty in supplies; assets intensity favoring upstream suppliers that tend to be more focused and have greater economies of scale; standardization; 1. 3 SUPPLY CHAINS: NEEDS AND RISKS 11 profitability; technological change; and scale and balance (economy and scope)... meet both quality standards and objectives (Reyniers and Tapiero 19 95a, 19 95b; Tapiero 19 95, 19 96, 2006) 24 1 SUPPLY CHAIN OPERATIONS MANAGEMENT For discussion purposes, we shall consider a number of cases which will be outlined and dealt with in far greater detail in Chapter 8, devoted to quality and its control in supply chains Consider supplier-producer relationships, franchises and situations where... its own right 22 1 SUPPLY CHAIN OPERATIONS MANAGEMENT Full Control And Monitoring Centralized organization And management Figure 1. 9 Inventory Management in Vertical-Horizontal SC Figure 1. 10 Inventory and Outsourcing What are the rules of leadership? Who is leading? Who has the information? Who has the power and can exercise it or not? What are the supply priorities, guarantees and related issues . operations management 12 1. 5 Supply chains and inventory management 16 1. 6 Quality and supply chain management 23 1. 7 Games and supply chain management 29 1. 8 Risk and supply chain management 35. chain operations management 3 1. 1 Supply chain operations: a metamorphosis 4 1. 2 Motivations and organization 5 1. 3 Supply chains: needs and risks 10 1. 4 Supply chains and operations management. Risk and Supply Chain Management xi PART I SUPPLY CHAINS AND OPERATIONS MODELING AND MANAGEMENT 1 SUPPLY CHAIN OPERATIONS MANAGEMENT Operations and industrial modelling and