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In the field of mathematical optimization, stochastic programming is a framework for modeling optimization problems that involve uncertainty. Whereas deterministic optimization problems are formulated with known parameters, real world problems almost invariably include some unknown parameters. When the parameters are known only within certain bounds, one approach to tackling such problems is called robust optimization. Here the goal is to find a solution which is feasible for all such data and optimal in some sense. Stochastic programming models are similar in style but take advantage of the fact that probability distributions governing the data are known or can be estimated. The goal here is to find some policy that is feasible for all (or almost all) the possible data instances and maximizes the expectation of some function of the decisions and the random variables. More generally, such models are formulated, solved analytically or numerically, and analyzed in order to provide useful information to a decision-maker. As an example, consider two-stage linear programs. Here the decision maker takes some action in the first stage, after which a random event occurs affecting the outcome of the first-stage decision. A recourse decision can then be made in the second stage that compensates for any bad effects that might have been experienced as a result of the first-stage decision. The optimal policy from such a model is a single first-stage policy and a collection of recourse decisions (a decision rule) defining which second-stage action should be taken in response to each random outcome. Stochastic programming has applications in a broad range of areas ranging from finance to transportation to energy optimization.〔 Stein W. Wallace and William T. Ziemba (eds.). ''Applications of Stochastic Programming''. MPS-SIAM Book Series on Optimization 5, 2005. 〕〔 Applications of stochastic programming are described at the following website, (Stochastic Programming Community ). 〕 This article includes an example of optimizing an investment portfolio over time. == Two-Stage Problems== The basic idea of two-stage stochastic programming is that (optimal) decisions should be based on data available at the time the decisions are made and should not depend on future observations. Two-stage formulation is widely used in stochastic programming. The general formulation of a two-stage stochastic programming problem is given by: where is the optimal value of the second-stage problem The classical two-stage linear stochastic programming problems can be formulated as 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「stochastic programming」の詳細全文を読む スポンサード リンク
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