Spatial Data Management

Contents......Page 6
Introduction......Page 10
 Newsvendor Problem......Page 12
 EOQ Model......Page 13
 Price Considerations......Page 14
 Continuous Production of Several Products......Page 16
 Lead Time......Page 17
 Random Demand Rate: Unsatisfied Demand Lost......Page 20
 Notation......Page 22
 Chapman-Kolmogorov Equations......Page 23
 Solution of Analytic Problems......Page 24
 Ergodic Theory......Page 27
 Examples......Page 30
 Deterministic Case......Page 34
 Stochastic Case: General Formulation......Page 35
 Functional Equation......Page 39
 Probabilistic Interpretation......Page 42
 Uniqueness......Page 46
 No Shortage Allowed.......Page 50
 Backlog Allowed......Page 55
 Deterministic Case......Page 60
 Finite Number of States......Page 62
 Ergodic Control of Inventories With no Shortage......Page 68
 Ergodic Control of Inventories With Backlog......Page 72
 Deterministic Case......Page 75
 Dynamic Programming......Page 76
 Interpretation......Page 78
 Penalty Approximation......Page 81
 Ergodic Case......Page 83
 Description of the Model......Page 88
 Another Formulation......Page 90
 Probabilistic Interpretation......Page 95
 Deterministic Model......Page 98
 Inventory Control With Fixed Cost and no Shortage......Page 103
 Inventory Control With Fixed Cost and Backlog......Page 123
 Deterministic Case......Page 142
 Ergodic Inventory Control With Fixed Cost and no Shortage......Page 144
 Ergodic Inventory Control With Fixed Cost and Backlog......Page 153
 Capacitated Inventory Management......Page 164
 Multi Supplier Problem......Page 168
 No Backlog and no Set-Up Cost......Page 178
 Backlog and no Set Up Cost......Page 192
 No Backlog and Set Up Cost......Page 203
 Backlog and Set Up Cost......Page 209
 Learning Process......Page 216
 Models With Inventory Position......Page 220
 Models Without Inventory Position......Page 227
 Information Delays......Page 236
 Ergodic Control With Information Delays......Page 241
 Deterministic Model......Page 256
 Ergodic Problem......Page 260
 Continuous Rate Delivery......Page 261
 Lead Time......Page 262
 Newsvendor Problem......Page 263
 Poisson Demand......Page 264
 Ergodic Case for the Poisson Demand......Page 272
 Poisson Demand With Lead Time......Page 274
 Ergodic Approach for Poisson Demand With Lead Time......Page 281
 Poisson Demand With Lead Time: Use of Inventory Position......Page 288
 Ergodic Theory for Lead Time With Inventory Position......Page 290
 Problem Formulation......Page 296
 s, S Policy......Page 298
 Solving the Q.V.I......Page 305
 Ergodic Theory......Page 307
 Probabilistic Interpretation......Page 312
 Description of the Problem......Page 334
 s, S Policy......Page 336
 Solution of the Q.V.I......Page 348
 The Problem......Page 350
 a, A, b, B Policy......Page 352
 Solution of the Q.V.I.......Page 360
 Computational Aspects......Page 362
Bibliography......Page 370
 Proof of Lemmas......Page 372
 Proof of Measurable Selection......Page 373
 Extension to U non Compact......Page 377
 Compactness Properties......Page 378