Stochastic Programs with First-Order Dominance Constraints Induced by Mixed-Integer Linear Recourse

We propose a new class of stochastic integer programs whose special features are dominance constraints induced by mixed-integer linear recourse. For these models, we establish closedness of the constraint set mapping with the underlying probability measure as a parameter. In the case of finite probability spaces, the models are shown to be equivalent to large-scale, block-structured, mixed-integer linear programs. We propose a decomposition algorithm for the latter and discuss computational results.