Markovian Demand Inventory Models

Online-Ressource (digital)

International Series in Operations Research & Management Science ; 108

Includes bibliographical references and index

Table of Contents; List of Figures; List of Tables; Preface; Notation; I Introduction; 1. Introduction; 1.1 Characteristics of Inventory Systems; 1.2 Brief Historical Overview of Inventory Theory; 1.3 Examples of Markovian Demand Models; 1.4 Contributions; 1.5 Plan of the Book; II Discounted Cost Models; 2. Discounted Cost Models with Backorders; 2.1 Introduction; 2.2 Review of the Related Literature; 2.3 Formulation of the Model; 2.4 Dynamic Programming and Optimal Feedback Policy; 2.5 Optimality of (s,S)-type Ordering Policies; 2.6 Nonstationary Infinite Horizon Problem

2.7 Cyclic Demand Model2.8 Constrained Models; 2.9 Concluding Remarks and Notes; 3. Discount Cost Models with Polynomially Growing Surplus Cost; 3.1 Introduction; 3.2 Formulation of the Model; 3.3 Dynamic Programming and Optimal Feedback Policy; 3.4 Nonstationary Discounted Infinite Horizon Problem; 3.5 Optimality of (s,S)-type Ordering Policies; 3.6 Stationary Infinite Horizon Problem; 3.7 Concluding Remarks and Notes; 4. Discounted Cost Models with Lost Sales; 4.1 Introduction; 4.2 Formulation of the Model; 4.3 Optimality of (s,S)-type Ordering Policies; 4.4 Extensions

4.5 Numerical Results4.6 Concluding Remarks and Notes; III Average Cost Models; 5. Average Cost Models with Backorders; 5.1 Introduction; 5.2 Formulation of the Model; 5.3 Discounted Cost Model Results from Chapter 2; 5.4 Limiting Behavior as the Discount Factor Approaches 1; 5.5 Vanishing Discount Approach; 5.6 Verification Theorem; 5.7 Concluding Remarks and Notes; 6. Average Cost Models with Polynomially Growing Surplus Cost; 6.1 Formulation of the Problem; 6.2 Behavior of the Discounted Cost Model with Respectto the Discount Factor; 6.3 Vanishing Discount Approach

6.4 Verification Theorem6.5 Concluding Remarks and Notes; 7. Average Cost Models with Lost Sales; 7.1 Introduction; 7.2 Formulation of the Model; 7.3 Discounted Cost Model Results from Chapter 4; 7.4 Limiting Behavior as the Discount Factor Approaches 1; 7.5 Vanishing Discount Approach; 7.6 Verification Theorem; 7.7 Concluding Remarks and Notes; IV Miscellaneous; 8. Models with Demand Influenced by Promotion; 8.1 Introduction; 8.2 Formulation of the Model; 8.3 Assumptions and Preliminaries; 8.4 Structural Results; 8.5 Extensions; 8.6 Numerical Results; 8.7 Concluding Remarks and Notes

9. Vanishing Discount Approach vs. Stationary Distribution Approach9.1 Introduction; 9.2 Statement of the Problem; 9.3 Review of Iglehart (1963b); 9.4 An Example; 9.5 Asymptotic Bounds on the Optimal Cost Function; 9.6 Review of the Veinott and Wagner Paper; 9.7 Existence of Minimizing Values of s and S; 9.8 Stationary Distribution Approach versus Dynamic Programming and Vanishing Discount Approach; 9.9 Concluding Remarks and Notes; V Conclusions and Open Research Problems; 10. Conclusions and Open Research Problems; VI Appendices; A. ANALYSIS; A.1 Continuous Functions on Metric Spaces

A.2 Convergence of a Sequence of Functions

10.1007/978-0-387-71604-6 [DOI]

ECONIS - Online Catalogue of the ZBW