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: The present article gives an overview over a second strand of the recent literature, namely methods that preserve the multi-objective nature of the problem during the computational analysis, including publications assuming a risk-neutral decision maker, but also articles addressing the situation where the decision maker is risk-averse.
Abstract: Currently, stochastic optimization on the one hand and multi-objective optimization on the other hand are rich and well-established special fields of Operations Research. Much less developed, however, is their intersection: the analysis of decision problems involving multiple objectives and stochastically represented uncertainty simultaneously. This is amazing, since in economic and managerial applications, the features of multiple decision criteria and uncertainty are very frequently co-occurring. Part of the existing quantitative approaches to deal with problems of this class apply scalarization techniques in order to reduce a given stochastic multi-objective problem to a stochastic single-objective one. The present article gives an overview over a second strand of the recent literature, namely methods that preserve the multi-objective nature of the problem during the computational analysis. We survey publications assuming a risk-neutral decision maker, but also articles addressing the situation where the decision maker is risk-averse. In the second case, modern risk measures play a prominent role, and generalizations of stochastic orders from the univariate to the multivariate case have recently turned out as a promising methodological tool. Modeling questions as well as issues of computational solution are discussed.
124 citations
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TL;DR: The paper presents a multi-stage stochastic programming formulation for the planning of clinical trials in the pharmaceutical research and development (R&D) pipeline that employs a reduced set of scenarios without compromising the quality of uncertainty representation.
124 citations
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TL;DR: An efficient framework, consisting of two stages, is presented here for the optimization of the reliability of a base-isolated structure considering future near-fault ground motions.
124 citations
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TL;DR: A dual-based procedure is presented and it is indicated how the dual-descent and primal-dual adjustment procedures proposed by D. Erlenkotter in the static case can be made monotonically improving in the stochastic case.
Abstract: In this paper, we study how the uncapacitated facility location problem is transformed into a two-stage stochastic program with recourse when uncertainty on demand, selling prices, production and transportation costs are introduced. We then present a dual-based procedure and indicate how the dual-descent and primal-dual adjustment procedures proposed by D. Erlenkotter (1978) in the static case can be made monotonically improving in the stochastic case. Results of computer experiments are reported.
124 citations
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TL;DR: In this article, the authors used nonlinear simulation-regression applied to a transient groundwater flow model to estimate parameter values and their uncertainties and use steady state flow path analyses to confirm the model's consistency with the location of contaminants.
Abstract: groundwater management model is developed for a shallow, unconfined sandy aquifer at a Superfund site at which a vinyl chloride plume is migrating toward Lake Michigan. We use nonlinear simulation-regression applied to a transient groundwater flow model to estimate parameter values and their uncertainties and use steady state flow path analyses to confirm the model's consistency with the location of contaminants. Parameter uncertainty is translated into flow model prediction uncertainty using a first-order Taylor series approximation. Optimal minimum-pumping strategies for steady state hydraulic containment of the plume are designed, and model prediction uncertainty is accounted for with stochastic programming. It is impossible to achieve a reliability level higher than 60% using only two pumping wells. For the 10-well case, pumping rates must increase about 40% to extend reliability from 50 to 90%. Monte Carlo analyses indicate that for the I 0-well 90% reliability formulation, the first-order method of propagating uncertainty results in a solution with accurate performance reliabilities. We find that the coefficient of variation in hydraulic gradient dictates whether the probabilistic constraints are obeyed. Comparison of the probabilistic constraint and "safety factor" approaches to overcoming model uncertainty reveals that the ability of probabilistic constraints to accommodate local variations in model prediction uncertainty is highly important. Postoptimization solute transport studies show that increased reliability levels for hydraulic containment do not necessarily translate into faster plume cleanup times.
124 citations