Markovian Demand Inventory Models

Inventory management is concerned with matching supply with demand and a central problem in Operations Management. The problem is to find the amount to be produced or purchased in order to maximize the total expected profit or minimize the total expected cost. Over the past two decades, several variations of the formula appeared, mostly in trade journals written by and for inventory managers. A critical assumption in the inventory literature is that the demands in different periods are independent and identically distributed. However, in real life, demands may depend on environmental considerations or the events in the world such as the weather, the state of economy, etc. Moreover, these events are represented by stochastic processes - exogenous or controlled.

In Markovian Demand Inventory Models, the authors are concerned with inventory models where these world events are modeled by Markov processes. Their research on Markovian demand inventory models was carried out over a period of ten years beginning in the early nineties.

"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