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Miguel Lejeune (mlejeunegwu.edu) Abstract: optimization problems in which the random variables are represented by an extremely large number of scenarios. The method involves the binarization of the probability distribution, and the generation of a consistent partially defined Boolean function (pdBf) representing the combination (F,p) of the binarized probability distribution F and the enforced probability level p. We show that the pdBf representing (F,p) can be compactly extended as a disjunctive normal form (DNF). The DNF is a collection of combinatorial ppatterns, each of which defining sufficient conditions for a probabilistic constraint to hold. We propose two linear programming formulations for the generation of ppatterns which can be subsequently used to derive a linear programming inner approximation of the original stochastic problem. A formulation allowing for the concurrent generation of a ppattern and the solution of the deterministic equivalent of the stochastic problem is also proposed. Results show that largescale stochastic problems, in which up to 50,000 scenarios are used to describe the stochastic variables, can be consistently solved to optimality within a few seconds. Keywords: Programming: stochastic; Probability; Combinatorial Pattern; Probabilistic Constraint; Boolean Programming Category 1: Stochastic Programming Citation: To appear in Operations Research. Download: [PDF] Entry Submitted: 08/20/2010 Modify/Update this entry  
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