Topic
Stochastic programming
About: Stochastic programming is a research topic. Over the lifetime, 12343 publications have been published within this topic receiving 421049 citations.
Papers published on a yearly basis
Papers
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TL;DR: In this article, the essential elements of semidenite programming as a computational tool for the analysis of systems and control problems are presented, with particular emphasis on general duality properties such as providing suboptimality or infeasibility certicates.
127 citations
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TL;DR: It is shown that for a broad class of 2-stage linear models with recourse, one can, for any ε > 0, in time polynomial in 1/ε and the size of the input, compute a solution of value within a factor of the optimum, in spite of the fact that exponentially many second-stage scenarios may occur.
Abstract: Stochastic optimization problems attempt to model uncertainty in the data by assuming that the input is specified by a probability distribution. We consider the well-studied paradigm of 2-stage models with recourse: first, given only distributional information about (some of) the data one commits on initial actions, and then once the actual data is realized (according to the distribution), further (recourse) actions can be taken. We show that for a broad class of 2-stage linear models with recourse, one can, for any e > 0, in time polynomial in 1/e and the size of the input, compute a solution of value within a factor (1pe) of the optimum, in spite of the fact that exponentially many second-stage scenarios may occur. In conjunction with a suitable rounding scheme, this yields the first approximation algorithms for 2-stage stochastic integer optimization problems where the underlying random data is given by a “black box” and no restrictions are placed on the costs in the two stages. Our rounding approach for stochastic integer programs shows that an approximation algorithm for a deterministic analogue yields, with a small constant-factor loss, provably near-optimal solutions for the stochastic generalization. Among the range of applications, we consider are stochastic versions of the multicommodity flow, set cover, vertex cover, and facility location problems.
127 citations
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TL;DR: The joint optimisation for both the inventory control of the spare parts and the Preventive Maintenance inspection interval is presented and the delay-time concept developed for inspection modelling is used to construct the probabilities of the number of failures and theNumber of the defective items identified at a PM epoch.
127 citations
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01 May 1994
TL;DR: New models of fuzzy multicriteria, discrete, geometric, fractioned, dynamic and stochastic programming are discussed and relations to genetic algorithms, simulated annealing and neural networks presented in the book may lead to a new generation of fuzzy optimization models.
Abstract: The purpose of this text is to provide a comprehensive exposition of relevant recent developments in the field of broadly perceived fuzzy optimization. New models of fuzzy multicriteria, discrete, geometric, fractioned, dynamic and stochastic programming are discussed. Relations to genetic algorithms, simulated annealing and neural networks presented in the book may lead to a new generation of fuzzy optimization models.
126 citations
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TL;DR: In this article, a stochastic linear programming model is proposed within a single-period planning framework to maximize the expected profit for a biofuel supply chain under demand and price uncertainties.
126 citations