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.

我们考虑在Wasserstein模糊度集上具有随机右手边的分布健壮的机会受限程序（DR-CCP）的精确确定性混合整数编程（MIP）公式。已知现有的MIP公式具有较弱的连续弛豫范围，因此，对于半径较小或问题大小较大的硬实例，即使在经过数小时的计算后，基于分支定界的求解过程仍存在较大的最优缺口。这极大地阻碍了DR-CCP范例的实际应用。受这些挑战的激励，我们进行了多面体研究以加强这些配方。我们揭示了DR-CCP及其标称对应项（样本平均近似值），混合集和健壮的0-1编程之间的一些隐藏连接。通过综合利用这些连接，我们为DR-CCP提供了改进的公式和两类有效不等式。我们用数字测试了结果对随机运输问题的影​​响。我们的实验证明了我们方法的有效性。特别是我们改进的公式和建议的有效不等式显着减少了整体求解时间。此外，这使我们能够通过将解决时间从几小时缩短到几秒钟，来显着扩大在此类DR-CCP配方中可以解决的问题规模。特别是我们改进的公式和建议的有效不等式显着减少了整体求解时间。此外，这使我们能够通过将解决时间从几小时缩短到几秒钟，来显着扩大在此类DR-CCP配方中可以解决的问题规模。特别是我们改进的公式和建议的有效不等式显着减少了整体求解时间。此外，这使我们能够通过将解决时间从几小时缩短到几秒钟，来显着扩大在此类DR-CCP配方中可以解决的问题规模。