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Mathematics - Probability Theory and Stochastic Processes | Introduction to Stochastic Programming

Introduction to Stochastic Programming

Birge, John R., Louveaux, François

1997, XIX, 421 p.

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The aim of stochastic programming is to find optimal decisions in problems which involve uncertain data. This field is currently developing rapidly with contributions from many disciplines including operations research, mathematics, and probability. Conversely, it is being applied in a wide variety of subjects ranging from agriculture to financial planning and from industrial engineering to computer networks. This textbook provides a first course in stochastic programming suitable for students with a basic knowledge of linear programming, elementary analysis, and probability. The authors aim to present a broad overview of the main themes and methods of the subject. Its prime goal is to help students develop an intuition on how to model uncertainty into mathematical problems, what uncertainty changes bring to the decision process, and what techniques help to manage uncertainty in solving the problems. The first chapters introduce some worked examples of stochastic programming and demonstrate how a stochastic model is formally built. Subsequent chapters develop the properties of stochastic programs and the basic solution techniques used to solve them. Three chapters cover approximation and sampling techniques and the final chapter presents a case study in depth. A wide range of students from operations research, industrial engineering, and related disciplines will find this a well-paced and wide-ranging introduction to this subject.

Content Level » Research

Keywords » Stochastic Programming - Stochastic model - linear optimization - model - modeling - nonlinear optimization - operations research - programming

Related subjects » Operations Research & Decision Theory - Probability Theory and Stochastic Processes

Table of contents 

I Models * Introduction and Examples * Uncertainty and Modeling Issues * II Basic Properties * Basic Properties and Theory * The Value of Information and the Stochastic Solution * III Solution Methods * Two-Stage Linear Recourse Problems * Nonlinear Programming Approaches to Two-Stage Recourse Problems * Multistage Stochastic Programs * Stochastic Integer Programs * IV Approximation and Sampling Methods * Evaluating and Approximating Expectations * Monte Carlo Methods * Multistage Approximations * V A Case Study * Capacity Expansion * Appendix: Sample Distribution Functions

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