From Encyclopedia of OR/MS, S. Gass and C. Harris (eds.) Stochastic Programming: Computational Issues and Challenges

Stochastic programming deals with a class of optimization models and algorithms in which some of the data may be subject to signi cant uncertainty. Such models are appropriate when data evolve over time and decisions need to be made prior to observing the entire data stream. For instance, investment decisions in portfolio planning problems must be implemented before stock performance can be observed. Similarly, utilities must plan power generation before the demand for electricity is realized. Such inherent uncertainty is ampli ed by technological innovation and market forces. As an example, consider the electric power industry. Deregulation of the electric power market, and the possibility of personal electricity generators (e.g. gas turbines) are some of the causes of uncertainty in the industry. Under these circumstances it pays to develop models in which plans are evaluated against a variety of future scenarios that represent alternative outcomes of data. Such models yield plans that are better able to hedge against losses and catastrophic failures. Because of these properties, stochastic programming models have been developed for a variety of applications, including electric power generation (Murphy et al [1982]), nancial planning (Cari~ no et al [1994]), telecommunications network planning (Sen et al [1994]), and supply chain management (Fisher et al [1997]), to mention a few. The widespread applicability of stochastic programming models has attracted considerable attention from the OR/MS community, resulting in several recent books (Kall and Wallace [1994], Birge and Louveaux [1997], Pr ekopa [1995]) and survey articles (Birge [1997], Sen and Higle [1999]). Nevertheless, stochastic programming models remain one of the more challenging optimization problems.