Chance-constrained set covering with Wasserstein ambiguity

We study a generalized distributionally robust chance-constrained set covering problem (DRC) with Wasserstein ambiguity set, where both decisions and uncertainty are binary-valued. establish the NP-hardness of DRC recast it as two-stage stochastic program, which facilitates decomposition algorithms. Furthermore, we derive two families valid inequalities. The first family targets hypograph “shifted” submodular function, is associated each scenario reformulation. show that inequalities give complete description convex hull hypograph. second mixes across multiple scenarios gains further strength via lifting. Our numerical experiments demonstrate out-of-sample performance model effectiveness our proposed reformulation