Beyer / Cheng / Sethi Markovian Demand Inventory Models

1. Auflage 2009
ISBN: 978-0-387-71604-6
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 108, 255 Seiten

Reihe: International Series in Operations Research & Management Science

This text provides a superbly researched insight into Markovian demand inventory models. The result of ten years of research, this work covers all aspects of demand inventory where they are modeled by Markov processes. Inventory management is concerned with matching supply with demand and is a central problem in Operations Management. The central problem is to find the amount to be produced or purchased in order to maximize the total expected profit, or minimize the total expected cost.

Autoren/Hrsg.

Beyer, Dirk

Cheng, Feng

Sethi, Suresh P.

Taksar, Michael

Inhaltsverzeichnis

1;Table of Contents;5
2;List of Figures;9
3;List of Tables;10
4;Preface;11
5;Notation;14
6;I Introduction;18
6.1;1. Introduction;19
6.1.1;1.1 Characteristics of Inventory Systems ;19
6.1.2;1.2 Brief Historical Overview of Inventory Theory ;21
6.1.3;1.3 Examples of Markovian Demand Models ;28
6.1.4;1.4 Contributions ;31
6.1.5;1.5 Plan of the Book ;32
7;II Discounted Cost Models;35
7.1;2. Discounted Cost Models with Backorders;36
7.1.1;2.1 Introduction ;36
7.1.2;2.2 Review of the Related Literature ;37
7.1.3;2.3 Formulation of the Model ;38
7.1.4;2.4 Dynamic Programming and Optimal Feedback Policy ;41
7.1.5;2.5 Optimality of (s,S)-type Ordering Policies ;46
7.1.6;2.6 Nonstationary Infinite Horizon Problem ;48
7.1.7;2.7 Cyclic Demand Model ;52
7.1.8;2.8 Constrained Models ;52
7.1.9;2.9 Concluding Remarks and Notes ;54
7.2;3. Discount Cost Models with Polynomially Growing Surplus Cost;56
7.2.1;3.1 Introduction ;56
7.2.2;3.2 Formulation of the Model ;57
7.2.3;3.3 Dynamic Programming and Optimal Feedback Policy ;59
7.2.4;3.4 Nonstationary Discounted Infinite Horizon Problem ;64
7.2.5;3.5 Optimality of (s,S)-type Ordering Policies ;70
7.2.6;3.6 Stationary Infinite Horizon Problem ;72
7.2.7;3.7 Concluding Remarks and Notes ;72
7.3;4. Discounted Cost Models with Lost Sales;74
7.3.1;4.1 Introduction ;74
7.3.2;4.2 Formulation of the Model ;75
7.3.3;4.3 Optimality of (s,S)-type Ordering Policies ;78
7.3.4;4.4 Extensions ;81
7.3.5;4.5 Numerical Results ;84
7.3.6;4.6 Concluding Remarks and Notes ;87
8;III Average Cost Models;96
8.1;5. Average Cost Models with Backorders;97
8.1.1;5.1 Introduction ;97
8.1.2;5.2 Formulation of the Model ;100
8.1.3;5.3 Discounted Cost Model Results from Chapter 2 ;103
8.1.4;5.4 Limiting Behavior as the Discount Factor Approaches 1 ;104
8.1.5;5.5 Vanishing Discount Approach ;112
8.1.6;5.6 Verification Theorem ;116
8.1.7;5.7 Concluding Remarks and Notes ;120
8.2;6. Average Cost Models with Polynomially Growing Surplus Cost;121
8.2.1;6.1 Formulation of the Problem ;121
8.2.2;6.2 Behavior of the Discounted Cost Model with Respectto the Discount Factor ;123
8.2.3;6.3 Vanishing Discount Approach ;130
8.2.4;6.4 Verification Theorem ;139
8.2.5;6.5 Concluding Remarks and Notes ;144
8.3;7. Average Cost Models with Lost Sales;146
8.3.1;7.1 Introduction ;146
8.3.2;7.2 Formulation of the Model ;146
8.3.3;7.3 Discounted Cost Model Results from Chapter 4 ;150
8.3.4;7.4 Limiting Behavior as the Discount Factor Approaches 1 ;151
8.3.5;7.5 Vanishing Discount Approach ;155
8.3.6;7.6 Verification Theorem ;158
8.3.7;7.7 Concluding Remarks and Notes ;163
9;IV Miscellaneous;164
9.1;8. Models with Demand Influenced by Promotion;165
9.1.1;8.1 Introduction ;165
9.1.2;8.2 Formulation of the Model ;167
9.1.3;8.3 Assumptions and Preliminaries ;174
9.1.4;8.4 Structural Results ;176
9.1.5;8.5 Extensions ;182
9.1.6;8.6 Numerical Results ;185
9.1.7;8.7 Concluding Remarks and Notes ;186
9.2;9. Vanishing Discount Approach vs. Stationary Distribution Approach;191
9.2.1;9.1 Introduction ;191
9.2.2;9.2 Statement of the Problem ;194
9.2.3;9.3 Review of Iglehart (1963b) ;196
9.2.4;9.4 An Example ;199
9.2.5;9.5 Asymptotic Bounds on the Optimal Cost Function ;204
9.2.6;9.6 Review of the Veinott and Wagner Paper ;207
9.2.7;9.7 Existence of Minimizing Values of s and S ;209
9.2.8;9.8 Stationary Distribution Approach versus Dynamic Programming and Vanishing Discount Approach ;215
9.2.9;9.9 Concluding Remarks and Notes ;218
10;V Conclusions and Open Research Problems;220
10.1;10. Conclusions and Open Research Problems;221
11;VI Appendices;224
11.1;A. ANALYSIS;225
11.1.1;A.1 Continuous Functions on Metric Spaces ;225
11.1.2;A.2 Convergence of a Sequence of Functions ;227
11.1.3;A.3 The Arzelà-Ascoli Theorems ;228
11.1.4;A.4 Linear Operators ;230
11.1.5;A.5 Miscellany ;231
11.2;B. PROBABILITY;233
11.2.1;B.1 Integrability ;233
11.2.2;B.2 Conditional Expectation ;234
11.2.3;B.3 Renewal Theorem ;235
11.2.4;B.4 Renewal Reward Processes ;235
11.2.5;B.5 Stochastic Dominance ;236
11.2.6;B.6 Markov Chains ;237
11.3;C. CONVEX, QUASI-CONVEX AND K-CONVEX FUNCTIONS;240
11.3.1;C.1 PF2 Density and Quasi-convex Functions ;240
11.3.2;C.2 Convex and K-convex Functions ;241
12;References;248
13;Copyright Permissions;254
14;Author Index ;256
15;Subject Index ;258