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We consider chance-constrained binary programs, where each row of theinequalities that involve uncertainty needs to be satisfied probabilistically.Only the information of the mean and covariance matrix is available, and wesolve distributionally robust chance-constrained binary programs (DCBP). Usingtwo different ambiguity sets, we equivalently reformulate the DCBPs as 0-1second-order cone (SOC) programs. We further exploit the submodularity of 0-1SOC constraints under special and general covariance matrices, and utilize thesubmodularity as well as lifting to derive extended polymatroid inequalities tostrengthen the 0-1 SOC formulations. We incorporate the valid inequalities in abranch-and-cut algorithm for efficiently solving DCBPs. We demonstrate thecomputational efficacy and solution performance using diverse instances of achance-constrained bin packing problem.

Ambiguous Chance-Constrained Binary Programs under Mean-Covariance Information