Integer Programming Approaches for Distributionally Robust Chance Constraints with Adjustable Risks

Abstract: We study distributionally robust chance-constrained programs (DRCCPs) with individual chance constraints under a Wasserstein ambiguity. The DRCCPs treat the risk tolerances associated with the distributionally robust chance constraints (DRCCs) as decision variables to trade off between the system cost and risk of violations by penalizing the risk tolerances in the objective function. The introduction of adjustable risks, unfortunately, leads to NP-hard optimization problems. We develop integer programming approaches for individual chance constraints with uncertainty either on the right-hand side or on the left-hand side. In particular, we derive mixed integer programming reformulations for the two types of uncertainty to determine the optimal risk tolerance for the chance constraint. Valid inequalities are derived to strengthen the formulations. We test diverse instances of diverse sizes.