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 multi-period multi-echelon forward-reverse logistics network design under risk model is developed in a stochastic mixed integer linear programming (SMILP) decision making form as a multi-stage stochastically program to maximize the total expected profit.
328 citations
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TL;DR: Computational results indicate that by using the strengthened formulations of PCLP, instances that are considerably larger than have been considered before can be solved to optimality.
Abstract: Linear programs with joint probabilistic constraints (PCLP) are difficult to solve because the feasible region is not convex. We consider a special case of PCLP in which only the right-hand side is random and this random vector has a finite distribution. We give a mixed-integer programming formulation for this special case and study the relaxation corresponding to a single row of the probabilistic constraint. We obtain two strengthened formulations. As a byproduct of this analysis, we obtain new results for the previously studied mixing set, subject to an additional knapsack inequality. We present computational results which indicate that by using our strengthened formulations, instances that are considerably larger than have been considered before can be solved to optimality.
327 citations
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TL;DR: Stochastic optimization problems involving stochastic dominance constraints are introduced and necessary and sufficient conditions of optimality and duality theory are developed and it is shown that the Lagrange multipliers corresponding to dominance constraint are concave nondecreasing utility functions.
Abstract: We introduce stochastic optimization problems involving stochastic dominance constraints. We develop necessary and sufficient conditions of optimality and duality theory for these models and show that the Lagrange multipliers corresponding to dominance constraints are concave nondecreasing utility functions. The models and results are illustrated on a portfolio optimization problem.
327 citations
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TL;DR: This study considers a risk-averse two-stage stochastic programming model, where the conditional-value-at-risk (CVaR) as the risk measure and constructs two decomposition algorithms based on the generic Benders-decomposition approach to solve problems in the presence of variability risk measures.
327 citations
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TL;DR: A novel divide-and-conquer algorithm for generating p-efficient points, used to transform the problem into a set of disjunctive, convex MIPs and handle dual-bounded chance constraints, is proposed.
Abstract: Astochastic, mixed-integer program (MIP) involving joint chance constraints is developed that generates least-cost vehicle redistribution plans for shared-vehicle systems such that a proportion of all near-term demand scenarios are met. The model aims to correct short-term demand asymmetry in shared-vehicle systems, where flow from one station to another is seldom equal to the flow in the opposing direction. The model accounts for demand stochasticity and generates partial redistribution plans in circumstances when demand outstrips supply. This stochastic MIP has a nonconvex feasible region. A novel divide-and-conquer algorithm for generating p-efficient points, used to transform the problem into a set of disjunctive, convex MIPs and handle dual-bounded chance constraints, is proposed. Assuming independence of random demand across stations, a faster cone-generation method is also presented. In a real-world application for a system in Singapore, the potential of redistribution as a fleet management strategy and the value of accounting for inherent stochasticities are demonstrated.
325 citations