Stochastic Programming Problems with Probability and Quantile Functions KIBZUN, Andrey I.

Stochastic Programming Problems with Probability and Quantile Functions, Andrey I. Kibzun and Yuri S. Kan, Moscow Aviation Institute, Moscow, Russia
Stochastic programming methods are used increasingly to help solve optimization problems in many areas of scientific research, business and industry. Until now, publications on the subject have been confined mainly to disparate sources, making this the first book to provide a unified and rigorous treatment. The probability function can be written formally as the expectation of the set indicator function. However, known optimization methods do not work because of the non smoothness of the indicator function. Specific methods are required for solving these problems. After presenting examples of various models for several applied problems the book covers basic theoretical results and differing methods for calculating probability and quantile functions. The final chapter describes and compares numerical algorithms for the solution of stochastic programming problems with probabilistic objectives. As well as providing a clear introduction to the subject, the authors comprehensively cover all major results in the area. Numerous examples, models and algorithms are given, taken mostly from real problems in business and engineering. The book will be of interest to advanced students and researchers in operations research, statistics, engineering and economics.
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