Topic
Stochastic programming
About: Stochastic programming is a research topic. Over the lifetime, 12343 publications have been published within this topic receiving 421049 citations.
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TL;DR: This paper develops for the first time a rigorous algorithmic procedure for determining a robust decision policy in response to any weighting of the scenarios.
Abstract: A common approach in coping with multiperiod optimization problems under uncertainty where statistical information is not really enough to support a stochastic programming model, has been to set up and analyze a number of scenarios. The aim then is to identify trends and essential features on which a robust decision policy can be based. This paper develops for the first time a rigorous algorithmic procedure for determining such a policy in response to any weighting of the scenarios. The scenarios are bundled at various levels to reflect the availability of information, and iterative adjustments are made to the decision policy to adapt to this structure and remove the dependence on hindsight.
1,321 citations
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01 Apr 1987
TL;DR: As one of the part of book categories, dynamic programming deterministic and stochastic models always becomes the most wanted book.
Abstract: If you really want to be smarter, reading can be one of the lots ways to evoke and realize. Many people who like reading will have more knowledge and experiences. Reading can be a way to gain information from economics, politics, science, fiction, literature, religion, and many others. As one of the part of book categories, dynamic programming deterministic and stochastic models always becomes the most wanted book. Many people are absolutely searching for this book. It means that many love to read this kind of book.
1,311 citations
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TL;DR: In this paper, an introduction to stochastic programming is presented, which is based on the idea of Stochastic Programming (SPP) and is used in our work.
Abstract: (1998). Introduction to Stochastic Programming. Journal of the Operational Research Society: Vol. 49, No. 8, pp. 897-898.
1,274 citations
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TL;DR: An algorithm for L-shaped linear programs which arise naturally in optimal control problems with state constraints and stochastic linear programs (which can be represented in this form with an infinite number of linear constraints) is given.
Abstract: This paper gives an algorithm for L-shaped linear programs which arise naturally in optimal control problems with state constraints and stochastic linear programs (which can be represented in this form with an infinite number of linear constraints). The first section describes a cutting hyperplane algorithm which is shown to be equivalent to a partial decomposition algorithm of the dual program. The two last sections are devoted to applications of the cutting hyperplane algorithm to a linear optimal control problem and stochastic programming problems.
1,264 citations
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TL;DR: This paper presents a methodology for the solution of multistage stochastic optimization problems, based on the approximation of the expected-cost-to-go functions of Stochastic dynamic programming by piecewise linear functions.
Abstract: This paper presents a methodology for the solution of multistage stochastic optimization problems, based on the approximation of the expected-cost-to-go functions of stochastic dynamic programming by piecewise linear functions. No state discretization is necessary, and the combinatorial "explosion" with the number of states (the well known "curse of dimensionality" of dynamic programming) is avoided. The piecewise functions are obtained from the dual solutions of the optimization problem at each stage and correspond to Benders cuts in a stochastic, multistage decomposition framework. A case study of optimal stochastic scheduling for a 39-reservoir system is presented and discussed.
1,230 citations