CVaR-Based Approximations of Wasserstein Distributionally Robust Chance Constraints with Application to Process Scheduling

Distributionally robust chance constrained programming is a stochastic optimization approach that considers uncertainty in model parameters as well as uncertainty in the underlying probability distribution. It ensures a specified probability of constraint satisfaction for any probability distribution from a defined ambiguity set. In this work, we consider Wasserstein ambiguity sets and derive tractable approximations of individual and joint distributionally robust chance constraints (DRCCs) based on the Worst-Case Conditional Value-at-Risk (WC-CVaR). We further prove that the proposed approximations are exact for individual DRCCs and for joint DRCCs if the scaling factors are simultaneously optimized. The effectiveness of the proposed approach is demonstrated in an illustrative example and in two comprehensive process scheduling cases. The computational results show that the WC-CVaR approximation exhibits significantly better out-of-sample performance than the commonly used Bonferroni approximation, which tends to be overconservative, and classical chance constrained programming.