Foundations of stochastic inventory theory / Evan L. Porteus.

Format:

Book

Author/Creator:

Porteus, Evan L.

Contributor:

Alumni and Friends Memorial Book Fund.

Language:

English

Subjects (All):

Inventory control--Statistical methods.

Inventory control.

Stochastic control theory.

Physical Description:

xx, 299 pages : illustrations ; 25 cm

Place of Publication:

Stanford, Calif. : Stanford Business Books, an imprint of Stanford University Press, [2002]

Summary:

This book has a dual purpose- serving as an advanced textbook designed to prepare doctoral students to do research on the mathematical foundations of inventory theory, and as a reference work for those already engaged in such research. All chapters conclude with exercises that either solidify or extend the concepts introduced.

Contents:

1 Two Basic Models 1

1.1 The EOQ Model 1

1.2 The Newsvendor Model 7

2 Recursion 27

2.1 Solving a Triangular System of Equations 27

2.2 Probabilistic Analysis of Models 28

2.3 Proof by Mathematical Induction 29

2.4 Shortest-Route Problems 29

2.5 Stochastic Shortest-Route Problems 32

2.6 Deterministic Production Planning 34

2.7 Knapsack Problems 35

3 Finite-Horizon Markov Decision Processes 41

3.1 Example: e-Rite-Way 42

3.2 General Vocabulary and Basic Results 47

4 Characterizing the Optimal Policy 57

4.1 Example: The Parking Problem 57

4.2 Dynamic Inventory Management 64

4.3 Preservation and Attainment 72

5 Finite-Horizon Theory 77

5.1 Finite-State and -Action Theory 77

5.2 Proofs for the Finite-State and -Action Case 83

5.3 Generalizations 86

5.4 Optimality of Structured Policies 87

6 Myopic Policies 91

6.1 General Approaches to Finding Solutions 92

6.2 Development 93

6.3 Application to Inventory Theory 96

6.4 Application to Reservoir Management 97

6.5 Extensions 98

7 Dynamic Inventory Models 103

7.1 Optimality of (s, S) Inventory Policies 103

7.2 Linear-Quadratic Model 111

8 Monotone Optimal Policies 119

8.1 Intuition 119

8.2 Lattices and Submodular Functions 122

8.3 A Dynamic Case 126

8.4 Capacitated Inventory Management 128

9 Structured Probability Distributions 133

9.1 Some Interesting Distributions 133

9.2 Quasi-K-Convexity 137

9.3 A Variation of the (s, S) Inventory Model 139

9.4 Generalized (s, S) Policies 143

10 Empirical Bayesian Inventory Models 151

10.1 Model Formulation 152

10.2 Conjugate Priors 155

10.3 Scalable Problems 159

10.4 Dimensionality Reduction 161

11 Infinite-Horizon Theory 167

11.1 Problem Formulation 167

11.2 Mathematical Preparations 170

11.3 Finite State and Action Theory 173

11.4 Generalizations 178

12 Bounds and Successive Approximations 181

12.1 Preliminary Results 182

12.2 Elimination of Nonoptimal Actions 184

12.3 Additional Topics 188

13 Computational Markov Decision Processes 193

13.1 Policy Iteration 193

13.2 Use of Linear Programming 195

13.3 Preparations for Further Analysis 197

13.4 Convergence Rates for Value Iteration 199

13.5 Bounds on the Subradius 201

13.6 Transformations 202

14 A Continuous Time Model 209

14.1 A Two-Product Production/Inventory Model 210

14.2 Formulation and Initial Analysis 211

14.3 Results 216

Appendix A Convexity 223

A.1 Basic Definitions and Results 223

A.2 Role of the Hessian 230

A.3 Generalizations of Convexity 234

Appendix B Duality 241

B.2 The Everett Result 245

B.3 Duality 250

Appendix C Discounted Average Value 261

C.1 Net Present Value 262

C.2 Discounted Average Value 264

C.3 Alternatives with Different Time Horizons 267

C.4 Approximating the DAV 268

C.5 Application to the EOQ Model 271

C.6 Random Cycle Lengths 273

C.7 Random-Yield EOQ Problem 274

Appendix D Preference Theory and Stochastic Dominance 279

D.2 Stochastic Dominance 282

D.3 How to Define Variability 286

D.4 Application to the Newsvendor Problem 287.

Notes:

Includes index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Alumni and Friends Memorial Book Fund.

ISBN:

0804743991

OCLC:

50479260