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Markovian Demand Inventory Models / by Dirk Beyer, Feng Cheng, Suresh P. Sethi, Michael Taksar

By: Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: International Series in Operations Research & Management Science ; 108 | SpringerLink BücherPublisher: Boston, MA : Springer-Verlag US, 2010Description: Online-Ressource (digital)ISBN:
  • 9780387716046
  • 9780387716039
  • 9781282509016
Subject(s): Additional physical formats: 9780387716039 | Buchausg. u.d.T.: Markovian Demand Inventory Models. 1. Ed. New York : Springer, 2010. XX, 253 SDDC classification:
  • 658.5
  • 330.0151 23
  • 658.78701519233 22
  • 650
MSC: MSC: *90-02 | 90B05 | 60K20 | 90C39RVK: RVK: SK 820LOC classification:
  • HD28-70
  • HF5691-5716
  • TS160
DOI: DOI: 10.1007/978-0-387-71604-6Online resources:
Contents:
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
Summary: I INTRODUCTION -- II DISCOUNTED COST MODELS -- Discounted Cost Models with Backorders -- Discount Cost Models with Polynomially Growing Surplus Cost -- Discounted Cost Models with Lost Sales -- III AVERAGE COST MODELS -- Average Cost Models with Backorders -- Average Cost Models with Polynomially Growing Surplus Cost -- Average Cost Models with Lost Sales -- IV MISCELLANEOUS -- Models with Demand Influenced by Promotion -- Vanishing Discount Approach Versus Stationary Distribution Approach -- V CONCLUSIONS AND OPEN RESEARCH PROBLEMS -- Conclusions and Open Research ProblemsSummary: "This book contains the most complete, rigorous mathematical treatment of the classical dynamic inventory model with stochastics demands that I am aware of. Emphasis is placed on a demand structure governed by a discrete time Markov chain. The state of the Markov chain determines the demand distribution for the period in question. Under this more general demand structure, (s,S) ordering policies are still shown to be optimal. The mathematical level is advanced and the book would be most appropriate for a specialized course at the Ph.D. level." Donald L. Iglehart Professor Emeritus of Operations Research, Stanford University "This book provides a comprehensive mathematical presentation of (s,S) inventory models and affords readers thorough coverage of the analytic tools used to establish theoretical results. Markovian demand models are central in the extensive scientific literature on inventory theory, and this volume reviews all the important conceptual developments of the subject." Harvey M. Wagner University of North Carolina at Chapel Hill "Beyer, Cheng, Sethi and Taksar have done a fine job of bringing together many of the central results about this important class of models. The book will be useful to anyone interested in inventory theory." Paul Zipkin Duke UniversityPPN: PPN: 1648639127Package identifier: Produktsigel: ZDB-2-SBE
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