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: A fuzzy simulation based genetic algorithm is designed for solving chance constrained programming from stochastic to fuzzy environments and some numerical examples are discussed.
624 citations
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TL;DR: A stochastic optimization approach for the storage and distribution problem of medical supplies to be used for disaster management under a wide variety of possible disaster types and magnitudes and can aid interdisciplinary agencies to both prepare and respond to disasters by considering the risk in an efficient manner.
623 citations
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TL;DR: It is shown that the structure of the optimal robust policy is of the same base-stock character as the optimal stochastic policy for a wide range of inventory problems in single installations, series systems, and general supply chains.
Abstract: We propose a general methodology based on robust optimization to address the problem of optimally controlling a supply chain subject to stochastic demand in discrete time. This problem has been studied in the past using dynamic programming, which suffers from dimensionality problems and assumes full knowledge of the demand distribution. The proposed approach takes into account the uncertainty of the demand in the supply chain without assuming a specific distribution, while remaining highly tractable and providing insight into the corresponding optimal policy. It also allows adjustment of the level of robustness of the solution to trade off performance and protection against uncertainty. An attractive feature of the proposed approach is its numerical tractability, especially when compared to multidimensional dynamic programming problems in complex supply chains, as the robust problem is of the same difficulty as the nominal problem, that is, a linear programming problem when there are no fixed costs, and a mixed-integer programming problem when fixed costs are present. Furthermore, we show that the optimal policy obtained in the robust approach is identical to the optimal policy obtained in the nominal case for a modified and explicitly computable demand sequence. In this way, we show that the structure of the optimal robust policy is of the same base-stock character as the optimal stochastic policy for a wide range of inventory problems in single installations, series systems, and general supply chains. Preliminary computational results are very promising.
619 citations
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TL;DR: A dynamic model of the THS powertrain is developed and then applied for model-based control development, and two control algorithms are introduced: one based on the stochastic dynamic programming method, and the otherbased on the equivalent consumption minimization strategy.
Abstract: Toyota hybrid system (THS) is used in the current best selling hybrid vehicle on the market-the Toyota Prius. This hybrid system contains a power-split planetary gear system which combines the benefits of series and parallel hybrid vehicles. In this paper, we developed a dynamic model of the THS powertrain and then apply it for model-based control development. Two control algorithms are introduced: one based on the stochastic dynamic programming method, and the other based on the equivalent consumption minimization strategy. Both approaches determine the engine power based on the overall vehicle efficiency and apply the electrical machines to optimize the engine operation. The performance of these two algorithms is assessed by comparing against the dynamic programming results, which are non-causal but provide theoretical benchmarks for other implementable control algorithms.
619 citations
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TL;DR: Cachon et al. as mentioned in this paper studied robust linear optimization problems with uncertainty regions defined by φ-divergences and showed that the robust counterpart of a linear optimization problem with φ divergence uncertainty is tractable for most of the choices of φ typically considered in the literature.
Abstract: In this paper we focus on robust linear optimization problems with uncertainty regions defined by φ-divergences for example, chi-squared, Hellinger, Kullback--Leibler. We show how uncertainty regions based on φ-divergences arise in a natural way as confidence sets if the uncertain parameters contain elements of a probability vector. Such problems frequently occur in, for example, optimization problems in inventory control or finance that involve terms containing moments of random variables, expected utility, etc. We show that the robust counterpart of a linear optimization problem with φ-divergence uncertainty is tractable for most of the choices of φ typically considered in the literature. We extend the results to problems that are nonlinear in the optimization variables. Several applications, including an asset pricing example and a numerical multi-item newsvendor example, illustrate the relevance of the proposed approach.
This paper was accepted by Gerard P. Cachon, optimization.
617 citations