Distributionally robust simple integer recourse with mean-MAD ambiguity set

Abstract We consider a two-stage distributionally robust simple integer recourse (DR-SIR) model with a mean-MAD ambiguity set. By leveraging infinite-dimensional linear programming duality and complementary slackness, we identify the worst-case distribution for every first-stage decision. These distributions turn out to be discrete with at most three realizations. Consequently, we are able to derive an expression for the worst-case expected cost function, which we denote as the DR-SIR function. This expression depends on the first-stage decision, the value of the mean absolute deviation, and several other conditions. In particular, depending on the specific case, the DR-SIR function is discontinuous, but may be linear or hyperbolic on parts of its domain. Numerical experiments show that the DR-SIR function is typically larger for larger values of the mean absolute deviation. Moreover, we find that DRO may have a significant convexifying effect on the second-stage value function, in particular for medium values of the mean absolute deviation.