1 Introduction 1. 2 Forecasting and Demand Modeling 5. 3 Deterministic Inventory Models Stochastic Inventory Models 63

Transcription

1 CONTENTS IN BRIEF 1 Introduction 1 2 Forecasting and Demand Modeling 5 3 Deterministic Inventory Models 29 4 Stochastic Inventory Models 63 5 Multi Echelon Inventory Models Dealing with Uncertainty in Inventory Optimization Facility Location Models Dealing with Uncertainty in Facility Location Process Flexibility The Bullwhip Effect Supply Chain Contracts Auctions 305 Appendix A: Multiple Chapter Problems 321 Appendix B: How to Write Proofs: A Short Guide 327 Appendix C: Helpful Formulas 337 Appendix D: Lagrangian Relaxation 341 Bibliography 349 vii

2

3 CONTENTS List of Figures List of Tables Preface xvii xxi xxiii 1 Introduction Overview of Supply Chain Management Levels of Decision Making in Supply Chain Management Applications of Supply Chain Management 3 2 Forecasting and Demand Modeling Introduction Classical Demand Forecasting Methods Moving Average Exponential Smoothing Linear Regression Demand Modeling Techniques Bass Diffusion Model The Model 13 ix

4 x CONTENTS Discrete Time Version Parameter Estimation Extensions Leading Indicator Approach Discrete Choice Models Introduction to Discrete Choice The Multinomial Logit Model Example Application to Supply Chain Management 23 Problems 24 3 Deterministic Inventory Models Introduction to Inventory Modeling Why Hold Inventory? Classifying Inventory Models Costs Inventory Level and Inventory Position Roadmap Continuous Review: The Economic Order Quantity Model Problem Statement Cost Function Optimal Solution Sensitivity to Q Order Lead Times Power of Two Policies The EOQ with Quantity Discounts The EOQ with Planned Backorders Periodic Review: The Wagner Whitin Model Problem Statement Dynamic Programming Algorithm Extensions 57 Problems 58 4 Stochastic Inventory Models Preliminaries Demand Processes Continuous Review: (r, Q) Policies Problem Statement Approximate Model with Continuous Distribution 67

5 CONTENTS xi EOQB Approximation Exact Model with Discrete Distribution Periodic Review with Zero Fixed Costs: Base Stock Policies Base Stock Policies Single Period: The Newsvendor Model Finite Horizon Infinite Horizon Periodic Review with Non Zero Fixed Costs: (s, S) Policies (s, S) Policies Single Period Finite Horizon Infinite Horizon Policy Optimality Zero Fixed Costs: Base Stock Policies Non Zero Fixed Costs: (s, S) Policies 100 Problems Multi Echelon Inventory Models Introduction Multi Echelon Network Topologies Stochastic vs. Guaranteed Service Stochastic Service Models Serial Systems Exact Approach for Serial Systems Heuristic Approach for Serial Systems Other Network Topologies Guaranteed Service Models Introduction Demand Single Stage Network Serial Systems Tree Systems Solution Method 134 Problems Dealing with Uncertainty in Inventory Optimization Introduction The Risk Pooling Effect 143

6 xii CONTENTS Overview Problem Statement Decentralized System Centralized System Comparison Magnitude of Risk Pooling Effect Final Thoughts Postponement Introduction Optimization Model Relationship to Risk Pooling Transshipments Introduction Problem Statement Expected Cost Benefits of Transshipments Introduction to Supply Uncertainty Inventory Models with Disruptions The EOQ Model with Disruptions The Newsvendor Problem with Disruptions Inventory Models with Yield Uncertainty The EOQ Model with Yield Uncertainty The Newsvendor Problem with Yield Uncertainty The Risk Diversification Effect Problem Statement Notation Optimal Solution Mean and Variance of Optimal Cost Supply Disruptions and Stochastic Demand 174 Problems Facility Location Models Introduction The Uncapacitated Fixed Charge Location Problem Problem Statement Formulation Solution Methods Lagrangian Relaxation 189

7 CONTENTS xiii Capacitated Version A Multi Echelon, Multi Commodity Model Introduction Problem Statement Formulation Lagrangian Relaxation 201 Problems Dealing with Uncertainty in Facility Location Introduction The Location Model with Risk Pooling Introduction Problem Statement Notation Objective Function NLIP Formulation Lagrangian Relaxation Column Generation Stochastic and Robust Location Models Introduction The Stochastic Fixed Charge Location Problem The Minimax Fixed Charge Location Problem A Facility Location Model with Disruptions Introduction Notation Formulation Lagrangian Relaxation Tradeoff Curves 235 Problems Process Flexibility Introduction Flexibility Design Guidelines A Process Flexibility Optimization Model Formulation Lagrangian Relaxation 249 Problems 251

8 xiv CONTENTS 10 The Bullwhip Effect Introduction Proving the Existence of the Bullwhip Effect Demand Signal Processing Rationing Game Order Batching Price Speculation Reducing the Bullwhip Effect Demand Signal Processing Rationing Game Order Batching Price Speculation Centralizing Demand Information Centralized System Decentralized System 273 Problems Supply Chain Contracts Introduction Introduction to Game Theory Notation Preliminary Analysis The Wholesale Price Contract The Buyback Contract The Revenue Sharing Contract The Quantity Flexibility Contract 296 Problems Auctions Introduction The English Auction Combinatorial Auctions The Combinatorial Auction Problem Solving the Set Packing Problem Truthful Bidding The Vickrey Clarke Groves Auction 313 Problems 317

9 CONTENTS xv Appendix A: Multiple Chapter Problems 321 Problems 321 Appendix B: How to Write Proofs: A Short Guide 327 B.1 How to Prove Anything 327 B.2 Types of Things You May Be Asked to Prove 329 B.3 Proof Techniques 331 B.3.1 Direct Proof 331 B.3.2 Proof by Contradiction 332 B.3.3 Proof by Mathematical Induction 333 B.3.4 Proof by Cases 334 B.4 Other Advice 334 Appendix C: Helpful Formulas 337 C.1 Standardizing Normal Random Variables 337 C.2 Loss Functions 338 C.2.1 General Distributions 338 C.2.2 Standard Normal Distribution 338 C.2.3 Non Standard Normal Distributions 338 C.3 Differentiation of Integrals 339 C.3.1 Variable of Differentiation Not in Integral Limits 339 C.3.2 Variable of Differentiation in Integral Limits 339 C.4 Geometric Series 339 C.5 Normal Distributions in Microsoft Excel 340 C.6 Partial Means 340 Appendix D: Lagrangian Relaxation 341 D.1 Overview 341 D.2 Bounds 342 D.3 Subgradient Optimization 344 D.4 Stopping Criteria 346 D.5 Other Problem Types 346 D.5.1 Inequality Constraints 347 D.5.2 Maximization Problems 347 D.6 Branch and Bound 347 D.7 Algorithm Summary 348

10 xvi CONTENTS Bibliography 349 Index 359

11 LIST OF FIGURES 1.1 Schematic diagram of supply chain network Supply chain Weight distribution Random demands with trend and seasonality Color TVs in the 1960s: Forecasts from Bass model and actual demands Bass diffusion curve An example of a leading indicator product Inventory curve EOQ inventory curve Fixed, holding, and total costs as a function of Q Total purchase cost c(q) for Example Total cost curves for all units quantity discount structure. 47 xvii

12 xviii LIST OF FIGURES 3.6 Total cost curves for incremental quantity discount structure Total purchase cost c(q) for modified all units discounts structure EOQB inventory curve Wagner Whitin network Inventory level (solid line) and inventory position (dashed line) under (r, Q) policy Expected inventory curve for (r, Q) policy DP results, K = 0: y t (x) DP results, K > 0: y t (x) Possible shapes of the function H(y) Non convexity of θ t (x) K convexity Properties of K convex functions from Lemma Proof of Lemma Multi echelon network topologies N stage serial system in stochastic service model Digital camera supply chain network Single stage network N stage serial system in guaranteed service model Feasible region for two stage system A counterexample to the all or nothing claim for tree systems Relabeling the network Example network for SSSPP DP algorithm Manufacturing process with postponement Possible realizations of transshipment and ending inventories EOQ inventory curve with disruptions EOQ inventory curve with yield uncertainty Facility location configurations. Squares represent facilities; circles represent customers. 184

13 LIST OF FIGURES xix 8.1 Proof of Theorem 8.1(c) Solution to problem (P j ) UFLP solution for 49 node data set UFLP solution for 49 node data set, after disruption of facility in Sacramento Reliable solution for 49 node data set Sample RFLP tradeoff curve Examples of flexibility configurations Two chaining structures Examples of different chaining structures for non homogeneous demand case Increase in order variability in upstream supply chain stages Serial supply chain network Bullwhip effect simulation Bullwhip effect caused by price fluctuations Wholesale price and profits as a function of buyback credit. 293

14

15 LIST OF TABLES 2.1 Bass model parameters Sample demands and stockouts Disruption costs for optimal DCs Bounds on variability increase: Decentralized vs. centralized Payoffs for a sample game Payoffs after implementing a contract Contracting notation summary Valuations that induce non truthful bidding Single item VCG auction: Example Two item VCG auction: Example. 316 xxi

16 FUNDAMENTALS OF SUPPLY CHAIN THEORY Lawrence V. Snyder Lehigh University Zuo Jun Max Shen University of California, Berkeley A JOHN WILEY & SONS, INC., PUBLICATION