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International Series in Operations Research & Management Science #108: Markovian Demand Inventory Modelsby Dirk Beyer
Synopses & Reviews
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. They demonstrate that the optimality of (s, S)-type policies, or base-stock policies (i.e., s = S) when there are no fixed ordering costs with the provision that the policy parameters s and S depend on the current state of the Markov process representing the environment. Models allowing backorders when the entire demand cannot be filled from the available inventory as well as those when the current demand is lost are considered. As for cost criteria, we treat both the minimization of the expected total discounted cost and the long-run average cost. The average-cost criterion is mathematically more difficult than the discounted cost criteria. Finally, we generalize the usual assumptions on holding and shortage costs and on demands that are made in the literature.
With a particular focus on inventory models where these world events are modeled by Markov processes, the authors present their research on Markovian demand inventory models, which 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
This text provides a superbly researched insight into Markovian demand inventory models. The result of ten years of research, this work covers all aspects of demand inventory where they are modeled by Markov processes. Inventory management is concerned with matching supply with demand and is a central problem in Operations Management. The central 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.
Table of Contents
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.
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