id: 05975512 dt: b an: 05975512 au: Bensoussan, Alain ti: Dynamic programming and inventory control. so: Studies in Probability, Optimization and Statistics 3. Amsterdam: IOS Press (ISBN 978-1-60750-769-7/hbk; 978-1-60750-770-3/ebook). vii, 369~p. EUR~135.00; \$~196.00 (2011). py: 2011 pu: Amsterdam: IOS Press la: EN cc: ut: dynamic programming; inventory control; Markov chains; stopping time; ergodic theory; optimal control; impulse control; random demand ci: li: doi:10.3233/978-1-60750-770-3-i ab: The book is a comprehensive overview of the theories of dynamic programming and inventory control. The novelty of this work is mainly provided by the detailed study of the probabilistic models, those that extend the classical deterministic models. The author carefully treats a variety of ergodic problems in the field of inventory control. Finite horizon problems are presented as approximations to infinite horizon problems. Let us take a look at the contents of this book. After a very good presentation of the specific treatment of the field of dynamic programming and inventory control provided by this work, the author briefly exposes a series of classical important {\it static problems} (starting with the {\it newsvendor problem}, the oldest problem in the area, and the {\it Economic Order Quantity} model). In Chapter 3 presents, in a modern way, the main properties of Markov chains. The ergodic theory is applied to some classical inventory problems. Chapter 4 is dedicated to the study of optimal control in discrete time. The {\it deterministic case} and the {\it probabilistic interpretation} (with {\it minimum solution} and {\it maximum solution}) are discussed. In Chapter 5, the general results of previous chapter are applied to the case of Inventory Control. This approach involves a special form of Bellman’s equation. Always, a control problem is considered with a {\it discount}$α<1$. The problem of Ergodic Control in discrete time, which corresponds to the case$α=1\$, is treated in Chapter 6. The situation where the decisions are stopping times is described in Chapter 7. The general technique of impulse control, developed in Chapter 8, is applied in the next two chapter to the situation of set up costs in inventory control. In Chapter 17 the author discusses two band impulse control. These studies request the presentation of {\it k-convexity theory}, as a useful mathematical tool. Chapters 11-16 further extend inventory problems in many important directions: dynamic inventory models, inventory control with Markov/diffusion demands, lead times and delays, continuous time inventory control and mean reverting inventory control. This work contains many original and refined proofs. The reading of the book is pleasant. The general theory is completed by interesting applications. Also, the reader is invited to solve a series of proposed exercises. The author displays a very good experience and erudition in the area. rv: Eugen Paltanea (Braşov)