Stochastic Programming Problems with Probability and Quantile Functions

The concept of a system as an entity in its own right has emerged with increasing force in the past few decades in, for example, the areas of electrical and control engineering, economics, ecology, urban structures, automaton theory, operational research and industry. The more definite concept of a large-scale system is implicit in these applications, but is particularly evident in fields such as the study of communication networks, computer networks and neural networks. The Wiley-Interscience Series in Systems and Optimization has been established to serve the needs of researchers in these rapidly developing fields. It is intended for works concerned with developments in quantitative systems theory, applications of such theory in areas of interest, or associated methodology. Of related interest Stochastic Programming Peter Kall, University of Zurich, Switzerland and Stein W. Wallace, University of Trondheim, Norway Stochastic Programming is the first textbook to provide a thorough and self-contained introduction to the subject. Carefully written to cover all necessary background material from both linear and non-linear programming, as well as probability theory, the book draws together the methods and techniques previously described in disparate sources. After introducing the terms and modelling issues when randomness is introduced in a deterministic mathematical programming model, the authors cover decision trees and dynamic programming, recourse problems, probabilistic constraints, preprocessing and network problems. Exercises are provided at the end of each chapter. Throughout, the emphasis is on the appropriate use of the techniques, rather than on the underlying mathematical proofs and theories, making the book ideal for researchers and students in mathematical programming and operations research who wish to develop their skills in stochastic programming. Stochastic Programming Models with Probability and QuantileObjective Functions.

Basic Properties of Probabilistic Problems.

Estimates and Bounds for Probabilities and Quantiles.

Methods and Algorithms for Solving Probabilistic Problems.

Notation List.

Index.

Andrey I. Kibzun and Yuri S. Kan are the authors of Stochastic Programming Problems with Probability and Quantile Functions, published by Wiley. 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. The concept of a system as an entity in its own right has emerged with increasing force in the past few decades in, for example, the areas of electrical and control engineering, economics, ecology, urban structures, automaton theory, operational research and industry. The more definite concept of a large-scale system is implicit in these applications, but is particularly evident in fields such as the study of communication networks, computer networks and neural networks. The Wiley-Interscience Series in Systems and Optimization has been established to serve the needs of researchers in these rapidly developing fields. It is intended for works concerned with developments in quantitative systems theory, applications of such theory in areas of interest, or associated methodology. Of related interest Stochastic Programming Peter Kall, University of Zürich, Switzerland and Stein W. Wallace, University of Trondheim, Norway Stochastic Programming is the first textbook to provide a thorough and self-contained introduction to the subject. Carefully written to cover all necessary background material from both linear and non-linear programming, as well as probability theory, the book draws together the methods and techniques previously described in disparate sources. After introducing the terms and modelling issues when randomness is introduced in a deterministic mathematical programming model, the authors cover decision trees and dynamic programming, recourse problems, probabilistic constraints, preprocessing and network problems. Exercises are provided at the end of each chapter. Throughout, the emphasis is on the appropriate use of the techniques, rather than on the underlying mathematical proofs and theories, making the book ideal for researchers and students in mathematical programming and operations research who wish to develop their skills in stochastic programming.