We study distributionally robust chance-constrained programming (DRCCP) optimization problems with data-driven Wasserstein ambiguity sets. The proposed algorithmic and reformulation framework applies to all types of distributionally robust chance-constrained optimization problems subjected to individual as well as joint chance constraints, with random right-hand side and technology vector, and under two types of uncertainties, called uncertain probabilities and continuum of realizations. For the uncertain probabilities (UP) case, we provide new mixed-integer linear programming reformulations for DRCCP problems. For the continuum of realizations case with random right-hand side, we propose an exact mixed-integer second-order cone programming (MISOCP) reformulation and a linear programming (LP) outer approximation. For the continuum of realizations (CR) case with random technology vector, we propose two MISOCP and LP outer approximations. We show that all proposed relaxations become exact reformulations when the decision variables are binary or bounded general integers. For DRCCP with individual chance constraint and random right-hand side under both the UP and CR cases, we also propose linear programming reformulations which need the ex-ante derivation of the worst-case value-at-risk via the solution of a finite series of linear programs determined via a bisection-type procedure. We evaluate the scalability and tightness of the proposed MISOCP and (MI)LP formulations on a distributionally robust chance-constrained knapsack problem.

我们研究数据驱动的Wasserstein模糊度集的分布鲁棒机会受限编程（DRCCP）优化问题。所提出的算法和重新制定框架适用于所有类型的，具有随机和右手随机变量和联合技术条件且受到两种不确定性的，受个体和联合机会约束影响的，分布鲁棒的机会受限优化问题，称为不确定概率和连续统的实现。对于不确定概率（UP）情况，我们为DRCCP提供了新的混合整数线性规划公式问题。对于具有右手边的连续实现情况，我们提出了精确的混合整数二阶锥规划（MISOCP）重新格式和线性规划（LP）外部逼近。对于带有随机技术向量的连续实现（CR）情况，我们提出了两种MISOCP和LP外部近似。我们表明，当决策变量是二进制或有界的一般整数时，所有提议的松弛都将成为精确的重新表述。对于DRCCP在UP和CR情况下都具有个别机会约束和随机右手的情况下，我们还提出了线性规划公式，该公式需要通过有限级数线性方程组的事前推导最坏情况的风险值通过二等分类型程序确定的程序。我们评估了在分布稳健的机会受限背包问题上提出的MISOCP和（MI）LP公式的可伸缩性和紧密性。