Distributionally Robust Linear and Discrete Optimization with Marginals

Louis Chen, Will Ma, Karthik Natarajan, David Simchi-Levi, Zhenzhen Yan

Abstract: In this paper, we study linear and discrete optimization problems in which the objective coefficients are random, and the goal is to evaluate a robust bound on the expected optimal value, where the set of admissible joint distributions is assumed to be specified only up to the marginals. We study a primal-dual formulation for this problem, and in the process, unify existing results with new results. We establish NP-hardness of computing the bound for general polytopes and identify two sufficient conditions: one based on a dual formulation and one based on sublattices that provide a class of polytopes where the robust bounds are efficiently computable. We discuss several examples and applications in areas such as scheduling.