Distributionally Robust Two-Stage Stochastic Programming
研究在随机参数分布未知时，如何构建基于Wasserstein距离和最优二次运输距离的模糊集，并开发切割平面算法求解两阶段线性补偿问题，对供应链分配问题有参考价值。
Distributionally robust optimization is a popular modeling paradigm in which the underlying distribution of the random parameters in a stochastic optimization model is unknown. Therefore, hedging against a range of distributions, properly characterized in an ambiguity set, is of interest. We study two-stage stochastic programs with linear recourse in the context of distributional ambiguity, and formulate several distributionally robust models that vary in how the ambiguity set is built. We focus on the Wasserstein distance under a $p$-norm, and an extension, an optimal quadratic transport distance, as mechanisms to construct the set of probability distributions, allowing the support of the random variables to be a continuous space. We study both unbounded and bounded support sets, and provide guidance regarding which models are meaningful in the sense of yielding robust first-stage decisions. We develop cutting-plane algorithms to solve two classes of problems, and test them on a supply-allocation problem. Our numerical experiments provide further evidence as to what type of problems benefit the most from a distributionally robust solution.