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)