NEW FORMULATIONS FOR OPTIMIZATION UNDER STOCHASTIC DOMINANCE CONSTRAINTS

Stochastic dominance constraints allow a decision maker to manage risk in an optimization setting by requiring his or her 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.