Inventory control. Models and methods
The book under review, as the title suggests, deals with standard inventory models and the ramifications. These models are appropriately formulated and the needed mathematical derivations are comprehensively described. Special emphasis is given to fundamentals. The authors seem to have achieved the desired purpose given in their closing remarks, which is to stimulate the reader to reflect on his own. The book consists of the following six Chapters: 1. Deterministic inventory models. 2. The Wilson model with Poisson demand. 3. Stochastic single period models. 4. Stochastic models with continuous review. 5. Stochastic models with periodic review. 6. Numerical methods. Chapter 1 contains eighteen sections and deals extensively with the deterministic models. Starting with the basic Wilson's lot size model it goes to answer several questions related to the optimal control of both single and multi-item inventory systems. Chapters 2 and 5 consider models with stochastic demand with emphasis on periodic review systems. Chapter 2 provides an introduction to Poisson process together with some generalizations and extends the simple Wilson model to cases with such random demands. Chapter 3 deals with single period models and, presents the classic `Newsboy problem'. Chapter 4 introduces Markov models of continuous review \((s,S)\) systems with Poisson demand. In the case of backorders, in addition to the method of state probabilities, the approach of dynamic programming is also discussed. Chapter 5 deals with the multi-period (periodic-review) models using the dynamic programming approach. The basic Arrow-Harris-Marschak (AHM) model is discussed in detail. Further the optimality of \((s_ n,S_ n)\) policy is examined and bounds for \(s_ n\) and \(S_ n\) are provided. Models with autocorrelated demand and inventory with forecast mechanism are also introduced. The last Chapter is devoted to numerical procedures. The general methods of Markov decision processes like value iteration, policy iteration and the bisection method of dynamic programming are discussed. In addition, a special method due to Federgruen and Zipkin to compute the optimal \((s,S)\) for the undiscounted AHM model with backorders is also given. The book concludes with literature on inventory control to which the present book is a welcome addition. It should be useful to students and practitioners of OR as well as economists.
scientific article; zbMATH DE number 484863