The book under review is an important contribution to the rapidly developing field of stochastic programming. It is primarily intended for researchers in operations research mathematics and statistics. The authors recommend it also as a textbook for advanced graduate and postgraduate courses. It focuses on theoretical foundations and major recent advances in selected areas of stochastic programming. It is partly written at the level of advanced research papers which requires the reader to be familiar with probability and statistics and with mathematical programming. To make the book accessible, the last chapter presents an extensive background material on optimization and convex analysis, on probability and functional analysis. The worked examples and numerous exercises delineate clearly the wide-ranging possibilities of applications of stochastic programming and, at the same time, they help to build an intuition how to model uncertainty within mathematical programs and how to interpret the obtained results. The book will thus certainly attract also the wide spectrum of readers whose main interests lie in possible exploitation of stochastic programming methodology.
The first chapter is devoted to modeling issues of stochastic programming. Various possibilities are explained on typical applications in inventory, multiproduct assembly, portfolio selection and supply chain network design. The second chapter deals with linear and nonlinear two-stage problems. Chapter 3 covers various aspects of multistage stochastic programming including nonanticipativity, duality and scenario tree formulation. Recent developments in stochastic programs with probability constraints are the content of Chapter 4. Chapter 5 provides an extensive exposition on solution technique and statistical inference based on sophisticated Monte Carlo schemes. Various problems of the risk averse optimization, which belongs at present to the main topics of the focused interest both in research and applications of stochastic programming, are detailed in Chapter 6.
As to the content, there is some overlapping with chapters 1, 2, 5 and 6 of the recent Handbook of Stochastic Programming [Zbl 0115.90001]. However, additional up-to-date results were included and the style of “lectures” is certainly preferable for those who wish to enter the field of stochastic programming and to be able to develop it.