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Distributionally robust chance-constrained programs (DR-CCP) over Wassersteinambiguity sets exhibit attractive out-of-sample performance and admitbig-$M$-based mixed-integer programming (MIP) reformulations with conicconstraints. However, the resulting formulations often suffer from scalabilityissues as sample size increases. To address this shortcoming, we derivestronger formulations that scale well with respect to the sample size. Ourfocus is on ambiguity sets under the so-called left-hand side (LHS)uncertainty, where the uncertain parameters affect the coefficients of thedecision variables in the linear inequalities defining the safety sets. Theinteraction between the uncertain parameters and the variable coefficients inthe safety set definition causes challenges in strengthening the originalbig-$M$ formulations. By exploiting the connection between nominalchance-constrained programs and DR-CCP, we obtain strong formulations withsignificant enhancements. In particular, through this connection, we derive alinear number of valid inequalities, which can be immediately added to theformulations to obtain improved formulations in the original space ofvariables. In addition, we suggest a quantile-based strengthening procedurethat allows us to reduce the big-$M$ coefficients drastically. Furthermore,based on this procedure, we propose an exponential class of inequalities thatcan be separated efficiently within a branch-and-cut framework. Thequantile-based strengthening procedure can be expensive. Therefore, for thespecial case of covering and packing type problems, we identify an efficientscheme to carry out this procedure. We demonstrate the computational efficacyof our proposed formulations on two classes of problems, namely stochasticportfolio optimization and resource planning.

Strong Formulations for Distributionally Robust Chance-Constrained Programs with Left-Hand Side Uncertainty under Wasserstein Ambiguity