  We consider exact deterministic mixed-integer programming (MIP)
reformulations of distributionally robust chance-constrained programs (DR-CCP)
with random right-hand sides over Wasserstein ambiguity sets. The existing MIP
formulations are known to have weak continuous relaxation bounds, and,
consequently, for hard instances with small radius, or with large problem
sizes, the branch-and-bound based solution processes suffer from large
optimality gaps even after hours of computation time. This significantly
hinders the practical application of the DR-CCP paradigm. Motivated by these
challenges, we conduct a polyhedral study to strengthen these formulations. We
reveal several hidden connections between DR-CCP and its nominal counterpart
(the sample average approximation), mixing sets, and robust 0-1 programming. By
exploiting these connections in combination, we provide an improved formulation
and two classes of valid inequalities for DR-CCP. We test the impact of our
results on a stochastic transportation problem numerically. Our experiments
demonstrate the effectiveness of our approach; in particular our improved
formulation and proposed valid inequalities reduce the overall solution times
remarkably. Moreover, this allows us to significantly scale up the problem
sizes that can be handled in such DR-CCP formulations by reducing the solution
times from hours to seconds.
