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Contents Preface xiii 1 Supply chain management 1 1.1 What do we mean by logistics? 1 1.1.1 Plan of the chapter 4 1.2 Structure of production/distribution networks 6 1.3 Competition factors, cost drivers, and strategy 9 1.3.1 Competition factors 9 1.3.2 Cost drivers 10 1.3.3 Strategy 13 1.4 The role of inventories 14 1.4.1 A classical model: Economic Order Quantity 15 1.4.2 Cycle vs. capacity induced stock 20 1.5 Dealing with uncertainty 21 1.5.1 Setting safety stocks 22 1.5.2 A two-stage decision process: production planning in an assemble-to-order environment 25 1.5.3 Inventory deployment 32 v vi CONTENTS 1.6 Physical flows and transportation 34 1.7 Time horizons and hierarchical levels 35 1.8 Decision approaches 36 1.9 Information flows and decision rights 37 1.10 Quantitative models and methods 39 1.11 For further reading 41 References 42 2 Network Design and Transportation 43 2.1 The role of intermediate nodes in a distribution network 45 2.1.1 The risk pooling effect: reducing the uncertainty level 45 2.1.2 The role of transit points in transportation optimization 48 2.2 Location and flow optimization models 58 2.2.1 The transportation problem 59 2.2.2 The minimum cost flow problem 61 2.2.3 The plant location problem 63 2.2.4 Putting it all together: 66 2.3 Models involving nonlinear costs 69 2.4 For Further Reading 74 References 75 3 Forecasting 77 3.1 Introduction 77 3.2 The variable to be predicted 79 3.2.1 The forecasting process 83 3.3 Metrics for forecast errors 88 3.3.1 The Mean Error 89 3.3.2 Mean Absolute Deviation 90 3.3.3 Root Mean Square Error 91 3.3.4 Mean Percentage Error and Mean Absolute Percentage Error 92 3.3.5 ME%, MAD%, RMSE% 95 3.3.6 U Theil?s statistic 97 3.3.7 Using metrics of forecasting accuracy 98 3.4 A classification of forecasting methods. 100 3.5 Moving Average 105 CONTENTS vii 3.5.1 The demand model 105 3.5.2 The algorithm 105 3.5.3 Setting the parameters 106 3.5.4 Drawbacks and limitations 108 3.6 Simple exponential smoothing 108 3.6.1 The demand model 108 3.6.2 The algorithm 111 3.6.3 Setting the parameter 116 3.6.4 Initialization 117 3.6.5 Drawbacks and limitations 121 3.7 Exponential Smoothing with Trend 121 3.7.1 The demand model 121 3.7.2 The algorithm 121 3.7.3 Setting the parameters 122 3.7.4 Initialization 123 3.7.5 Drawbacks and limitations 125 3.8 Exponential smoothing with seasonality 127 3.8.1 The demand model 127 3.8.2 The algorithm 128 3.8.3 Setting the parameters 130 3.8.4 Initialization 130 3.8.5 Drawbacks and limitations 132 3.9 Smoothing with seasonality and trend 133 3.9.1 The demand model 133 3.9.2 The algorithm 133 3.9.3 Initialization 134 3.10 Simple linear regression 136 3.10.1 Setting up data for regression 142 3.11 Forecasting new products 143 3.11.1 The Delphi method and the committee process. 144 3.11.2 Lancaster model: forecasting new products through products features. 148 3.11.3 The early sales model 149 3.12 The Bass model. 155 3.12.1 Limitations and drawbacks 162 References 163 4 Inventory management with certain demand 165 viii CONTENTS 4.1 Introduction 165 4.2 Economic Order Quantity 173 4.3 Robustness of EOQ model 185 4.4 Case of LT > 0: the (Q,R) model 187 4.5 Case of finite replenishment rate 189 4.6 Multi-item EOQ 191 4.6.1 The case of shared ordering costs 192 4.6.2 The multi-item case with a constraint on ordering capacity. 194 4.7 Case of nonlinear costs. 197 4.8 The case of variable demand with known variability 201 References 205 5 Inventory control: the stochastic case 207 5.1 Introduction 207 5.2 The newsvendor problem 218 5.2.1 Extensions of the Newsvendor problem 229 5.3 Multi-period problems 239 5.4 Fixed quantity: the (Q,R) model 241 5.4.1 Optimization of the (Q,R) model in case the stockout cost depends on the size of the stockout 248 5.4.2 (Q,R) system: case of constraint on the type II service level 253 5.4.3 Optimization of the (Q,R) model in case the cost of a stock-out depends on the occurrence of a stockout 256 5.4.4 (Q,R) system: case of constraint on type I service level 258 5.5 Periodic review: S and (s, S) policies 260 5.6 The S policy 262 5.7 The (s, S) policy 267 References 269 6 Managing inventories in multi-echelon supply chains 271 6.1 Introduction 271 6.2 Managing multi-echelon chains: Installation vs. Echelon Stock 277 CONTENTS ix 6.2.1 Features of Installation and Echelon Stock logics 279 6.3 Coordination in the supply chain: the Bullwhip effect. 292 6.4 A linear distribution chain with two echelons and certain demand 302 6.5 Arborescent chain with two echelons: transit point with uncertain demand 309 6.6 A two echelon supply chain in case of stochastic demand. 318 References 325 7 Incentives in the supply chain 327 7.1 Introduction 327 7.2 Decisions on price: double marginalization 329 7.2.1 the first best solution: the vertically integrated firm. 330 7.2.2 The vertically disintegrated case: independent manufacturer and retailer 331 7.2.3 A way out: designing incentive schemes. 336 7.3 Decision on price in a competitive environment 340 7.3.1 the vertically disintegrated supply chain: independent manufacturer and retailer 340 7.4 Decision on inventories: the Newsvendor problem 341 7.4.1 The first best solution: the vertically integrated firm. 342 7.4.2 The vertically disintegrated case: independent manufacturer and retailer. 343 7.4.3 A way out: designing incentives and re-allocating decision rights 344 7.5 Decision on effort to produce and sell the product. 351 7.5.1 The first best solution: the vertically integrated firm. 351 7.5.2 the vertically disintegrated case: independent retailer and manufacturers. 352 7.5.3 The case of efforts both at the upstream and downstream stage. 356 7.6 Concluding remarks 359 References 360 x CONTENTS 8 Vehicle Routing 361 8.1 Network routing problems 362 8.2 Solution methods for symmetric TSP 365 8.2.1 Nearest-neighbor heuristic 366 8.2.2 Insertion-based heuristics 367 8.2.3 Local search methods 369 8.3 Solution methods for basic VRP 373 8.3.1 Constructive methods for VRP 374 8.3.2 Decomposition methods for VRP: cluster first, route second 381 8.4 Additional features of real-life VRP 385 8.4.1 Constructive methods for the VRP with time windows 387 8.5 Final remarks 390 8.6 For further reading 390 References 391 Appendix A A Quick Tour of Probability and Statistics 393 A.1 Sample space, events, and probability 394 A.2 Conditional probability and independence 397 A.3 Discrete random variables 401 A.3.1 A few examples of discrete distributions 406 A.4 Continuous random variables 411 A.4.1 Some continuous distributions 416 A.5 Jointly distributed random variables 420 A.6 Independence, covariance, and conditional expectation 422 A.6.1 Independent random variables 422 A.6.2 Covariance and correlation 424 A.6.3 Distributions obtained from the normal and the central limit theorem 426 A.6.4 Conditional expectation 429 A.7 Stochastic processes 434 A.8 Parameter estimation 440 A.8.1 Sample covariance and correlation 443 A.8.2 Confidence intervals 449 A.9 Hypothesis testing 453 A.9.1 An example of non-parametric test: the chi-square test 456 CONTENTS xi A.9.2 Testing hypotheses about the difference in the mean of two populations 457 A.10 Simple linear regression 459 A.10.1 Best fitting by least squares 460 A.10.2 Analyzing properties of regression estimators 466 A.10.3 Confidence intervals and hypothesis testing for regression estimators 477 A.10.4 Performance measures for linear regression 479 A.10.5 Verification of the underlying assumptions 482 A.10.6 Using linear regression to model nonlinear relationships 485 A.11 For further reading 488 References 489 Appendix B An even Quicker Tour in Mathematical Programming 491 B.1 Role and limitations of optimization models 493 B.2 Optimization models 500 B.3 Convex sets and functions 504 B.4 Nonlinear programming 509 B.4.1 The case of inequality constraints 512 B.4.2 An economic interpretation of Lagrange multipliers: shadow prices 514 B.5 Linear programming 517 B.6 Integer linear programming 519 B.6.1 Branch and bound methods 521 B.6.2 Model building in integer programming 526 B.7 Elements of multi-objective optimization 529 B.8 For further reading 533 References 534
Library of Congress Subject Headings for this publication:
Network analysis (Planning) -- Mathematics.
Production scheduling -- Statistical methods.
Business logistics -- Statistical methods.
Traffic flow -- Mathematical models.
Physical distribution of goods -- Mathematics.
Distribution (Probabliity theory).