Foundations of stochastic inventory theory (Book, 2009) [WorldCat.org]
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Foundations of stochastic inventory theory
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Foundations of stochastic inventory theory

Author: Evan L Porteus
Publisher: Stanford, Calif. : Stanford Univ. Press, 2009.
Series: Stanford Business Books
Edition/Format:   Print book : EnglishView all editions and formats
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  Read more...

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Document Type: Book
All Authors / Contributors: Evan L Porteus
ISBN: 9780804743990 0804743991
OCLC Number: 740984647
Notes: 2005.
Description: XX, 299 Seiten : Diagramme.
Contents: 1 Two Basic Models 1 1.1 The EOQ Model ... 1 1.2 The Newsvendor Model ... 7 Exercises ... ... 16 References ... ... 25 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 Exercises ... 36 References ... .. ... 40 3 Finite-Horizon Markov Decision Processes 41 3.1 Example: e-Rite-Way ... ..42 3.2 General Vocabulary and Basic Results ... 47 Exercises ... 54 References ... ... ... 56 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 Exercises ... 73 References ... 76 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 Exercises ... 88 References ... ... . 90 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 Exercises ... ... . 100 References ...102 7 Dynamic Inventory Models 103 7.1 Optimality of (s, S) Inventory Policies ... 103 7.2 Linear-Quadratic Model ... 111 Exercises ... 115 References ... ... ... 118 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 Exercises ... . 131 References ... ... ... ... .. ...132 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 Exercises ... ...148 References . .. .. ... .. ... ... ...150 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 Exercises ...163 References ... ... ... ...166 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 Exercises ... ...178 References . .. .. ... ...180 12 Bounds and Successive Approximations 181 12.1 Preliminary Results ... 182 12.2 Elimination of Nonoptimal Actions ... 184 12.3 Additional Topics ...188 Exercises ... 190 References . ... ... ... .. ... ... ...192 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 Exercises ... 207 References .. ... ...208 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 Exercises ... ... 221 References... 221 Appendix A Convexity 223 A.1 Basic Definitions and Results ... .. . 223 A.2 Role of the Hessian ... 230 A.3 Generalizations of Convexity ... 234 Exercises . ... .. .. ... ... 235 References ... ... ... 239 Appendix B Duality 241 B.1 Basic Concepts ... ...241 B.2 The Everett Result ...245 B.3 Duality . ... 250 Exercises ...255 References... 260 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 Exercises ... ... 275 References ...278
Series Title: Stanford Business Books
Responsibility: Evan L. Porteus.

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"This book provides a comprehensive foundation for inventory theory. Amazingly, Evan Porteus is able to introduce and explain very complex concepts in simple and interesting ways. In providing the Read more...

 
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