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Jian Hu(jianhu2010u.northwestern.edu) Abstract: Stochastic dominance theory provides tools to compare random entities. When comparing random vectors (say X and Y ), the problem can be viewed as one of multicriterion decision making under uncertainty. One approach is to compare weighted sums of the components of these random vectors using univariate dominance. In this paper we propose new concepts of stochastically weighted dominance. The main idea is to treat the vector of weights as a random vector V. We show that such an approach is much less restrictive than the deterministic weighted approach. We further show that the proposed new concepts of stochastic dominance are representable by a finite number of (mixedinteger) linear inequalities when the distributions of X, Y and V have finite support. We discuss two applications to illustrate the usefulness of the stochastically weighted dominance concept. The first application discusses the effect of this notion on the feasibility regions of optimization problems. The second application presents a multicriterion staffing problem where the goal is to decide the allocation of servers between two M/M/c queues based on waiting times. The latter example illustrates the use of stochastically weighted dominance concept for a ranking of the alternatives. Keywords: Stochastic Programming, Stochastic Dominance, Risk Management, Chance Constraint, Integer Programming Category 1: Applications  OR and Management Sciences Category 2: Stochastic Programming Category 3: Other Topics (MultiCriteria Optimization ) Citation: IEMS Dept. Northwestern University, 2011 Download: [PDF] Entry Submitted: 04/09/2011 Modify/Update this entry  
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