Markovian Demand Inventory Models
"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 th
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Markovian Demand Inventory Models
Dirk Beyer • Feng Cheng Suresh P. Sethi • Michael Taksar
International Series in Operations Research & Management Science
Volume 108
For other titles published in this series, go to http://www.springer.com/series/6161
Dirk Beyer · Feng Cheng · Suresh P. Sethi · Michael Taksar
Markovian Demand Inventory Models
123
Dirk Beyer M-Factor 1400 Fashion Island Blvd. Suite 602 San Mateo CA 94404 USA [email protected]
Feng Cheng Federal Aviation Administration Office of Performance Analysis and Strategy 800 Independence Ave. S.W. Washington, D.C. 20591 USA [email protected]
Suresh P. Sethi School of Management, M/S SM30 The University of Texas at Dallas 800 W. Campbell Road, SM 30 Richardson, TX 75080-3021 USA [email protected]
Michael Taksar Department of Mathematics University of Missouri Rollins Road Columbia MO 65211 USA [email protected]
ISSN 0884-8289 ISBN 978-0-387-71603-9 e-ISBN 978-0-387-71604-6 DOI 10.1007/978-0-387-71604-6 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2009935383 c Springer Science+Business Media, LLC 2010 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Table of Contents
List of Figures List of Tables Preface Notation
Part 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
Part II
ix xi xiii xvii
3 3 5 12 15 16
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 Model 2.8 Constrained Models 2.9 Concluding Remarks and Notes
21 21 22 23 26 31 33 37 37 39
vi
Table of Contents
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
41 41 42 44 49 55
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