Second-Order Stochastic Dominance Constraints Induced by Mixed-Integer Linear Recourse

Abstract

We introduce stochastic integer programs with dominance constraints induced by mixed-integer linear recourse. Closedness of the constraint set mapping with respect to perturbations of the underlying probability measure is derived. For discrete probability measures, large-scale, block-structured,mixed-integer linear programming equivalents to the dominance constrained stochastic programs areidentified. For these models, a decomposition algorithm is proposed. Computational tests withinstances from power optimization and Sudoku puzzling conclude the paper.