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Markovian Demand Inventory Models
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Markovian Demand Inventory Models

Beyer, Dirk; Cheng, Feng; Sethi, Suresh P.; Taksar, Michael
ISBN-10: 0387716033
ISBN-13: 9780387716039

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Inventory management is concerned with matching supply with demand and a central problem in Operations Management. This text covers all aspects of demand inventory where they are modeled by Markov processes.
List of Figures
List of Tables
Preface
Notation
Introduction
Introduction
Characteristics of Inventory Systems
Brief Historical Overview of Inventory Theory
Examples of Markovian Demand Models
Contributions
Plan of the Book
Discounted Cost Models
Discounted Cost Models with Backorders
Introduction
Review of the Related Literature
Formulation of the Model
Dynamic Programming and Optimal Feedback Policy
Optimality of (s, S)-type Ordering Policies
Nonstationary Infinite Horizon Problem
Cyclic Demand Model
Constrained Models
Concluding Remarks and Notes
Discounted Cost Models with Polynomially Growing Surplus Cost
Introduction
Formulation of the Model
Dynamic Programming and Optimal Feedback Policy
Nonstationary Discounted Infinite Horizon Problem
Optimality of (s, S)-type Ordering Policies
Stationary Infinite Horizon Problem
Concluding Remarks and Notes
Discounted Cost Models with Lost Sales
Introduction
Formulation of the Model
Optimality of (s,S)-type Ordering Policies
Extensions
Numerical Results
Concluding Remarks and Notes
Average Cost Models
Average Cost Models with Backorders
Introduction
Formulation of the Model
Discounted Cost Model Results from Chapter 2
Limiting Behavior as the Discount Factor Approaches 1
Vanishing Discount Approach
Verification Theorem
Concluding Remarks and Notes
Average Cost Models with Polynomially Growing Surplus Cost
Formulation of the Problem
Behavior of the Discounted Cost Model with Respect to the Discount Factor
Vanishing Discount Approach
Verification Theorem
Concluding Remarks and Notes
Average Cost Models with Lost Sales
Introduction
Formulation of the Model
Discounted Cost Model Results from Chapter 4
Limiting Behavior as the Discount Factor Approaches 1
Vanishing Discount Approach
Verification Theorem
Concluding Remarks and Notes
Miscellaneous
Models With Demand Influenced By Promotion
Introduction
Formulation of the Model
Assumptions and Preliminaries
Structural Results
Extensions
Numerical Results
Concluding Remarks and Notes
Vanishing Discount Approach Vs. Stationary Distribution Approach
Introduction
Statement of the Problem
Review of Iglehart (1963b)
An Example
Asymptotic Bounds on the Optimal Cost Function
Review of the Veinott and Wagner Paper
Existence of Minimizing Values of s and S
Stationary Distribution Approach versus Dynamic Programming and Vanishing Discount Approach
Concluding Remarks and Notes<p>206</p><l>1</l><l>Part V</l>
Conclusions and Open Research Problems
Appendices
Analysis
Continuous Functions on Metric Spaces
Convergence of a Sequence of Functions
The Arzela-Ascoli Theorems
Linear Operators
Miscellany
Probability
Integrability
Conditional Expectation
Renewal Theorem
Renewal Reward Processes
Stochastic Dominance
Markov Chains
Convex, Quasi-Convex and K-Convex Functions
PF<sub>2</sub> Density and Quasi-convex Functions
Convex and K-convex Functions
References
Copyright Permissions
Author Index
Subject Index

List price: $159.00
Edition: 2010
Publisher: Springer
Binding: Trade Cloth
Pages: 255
Size: 6.50" wide x 9.75" long x 0.75" tall
Weight: 1.23 lbs.
Language: English

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