New Formulations for Optimization Under Stochastic Dominance Constraints

James Luedtke (jluedtkus.ibm.com)

Abstract: Stochastic dominance constraints allow a decision-maker to manage risk in an optimization setting by requiring their decision to yield a random outcome which stochastically dominates a reference random outcome. We present new integer and linear programming formulations for optimization under first and second-order stochastic dominance constraints, respectively. These formulations are more compact than existing formulations, and relaxing integrality in the first-order formulation yields a second-order formulation, demonstrating the tightness of this formulation. We also present a specialized branching strategy and heuristics which can be used with the new first-order formulation. Computational tests illustrate the potential benefits of the new formulations.

Keywords: Stochastic programming, stochastic dominance constraints, risk, probabilistic constraints, integer programming

Category 1: Stochastic Programming

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Entry Submitted: 11/12/2007
Entry Accepted: 11/12/2007
Entry Last Modified: 05/02/2008

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