Markovian Demand Inventory Models

Abstract

"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 University. Introduction -- Discounted Cost Models with Backorders -- Discount Cost Models with Polynomially Growing Surplus Cost -- Discounted Cost Models with Lost Sales -- Average Cost Models with Backorders -- Average Cost Models with Polynomially Growing Surplus Cost -- Average Cost Models with Lost Sales -- Models with Demand Influenced by Promotion -- Vanishing Discount Approach vs. Stationary Distribution Approach -- Conclusions and Open Research Problems -- Analysis -- Probability -- Convex, Quasi-Convex and K-Convex Functions -- References -- Copyright Permissions -- Author Index -- Subject Index.