  Inspired by its success for their continuous counterparts, the standard
approach to deal with mixed-integer recourse (MIR) models under distributional
uncertainty is to use distributionally robust optimization (DRO). We argue,
however, that this modeling choice is not always justified, since DRO
techniques are generally computationally extremely challenging when integer
decision variables are involved. That is why we propose a fundamentally
different approach for MIR models under distributional uncertainty aimed at
obtaining models with improved computational tractability. For the special case
of simple integer recourse (SIR) models, we show that tractable models can be
obtained by pragmatically selecting the uncertainty set. Here, we consider
uncertainty sets based on the Wasserstein distance and also on generalized
moment conditions. We compare our approach with standard DRO and discuss
potential generalizations of our ideas to more general MIR models. An important
side-result of our analysis is the derivation of performance guarantees for
convex approximations of SIR models. In contrast with the literature, these
error bounds are not only valid for continuous distribution, but hold for any
distribution.
