Distributionally robust chance-constrained programs with right-hand side uncertainty under Wasserstein ambiguity

Nam Ho-Nguyen, Fatma Kılınç-Karzan, Simge Küçükyavuz, Dabeen Lee*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)641-672
Number of pages32
JournalMathematical Programming
Issue number1-2
StatePublished - Nov 2022


  • Chance constraints
  • Distributionally robust
  • Mixing sets
  • Wasserstein ambiguity

ASJC Scopus subject areas

  • Software
  • General Mathematics


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