A Solution Approach to Distributionally Robust Joint-Chance-Constrained Assignment Problems

Shanshan Wang, Jinlin Li, Sanjay Mehrotra
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引用次数: 7

Abstract

We study the assignment problem with chance constraints (CAP) and its distributionally robust counterpart DR-CAP. We present a technique for estimating big-M in such a formulation that takes advantage of the ambiguity set. We consider a 0-1 bilinear knapsack set to develop valid inequalities for CAP and DR-CAP. This is generalized to the joint chance constraint problem. A probability cut framework is also developed to solve DR-CAP. A computational study on problem instances obtained from using real hospital surgery data shows that the developed techniques allow us to solve certain model instances and reduce the computational time for others. The use of Wasserstein ambiguity set in the DR-CAP model improves the out-of-sample performance of satisfying the chance constraints more significantly than the one possible by increasing the sample size in the sample average approximation technique. The solution time for DR-CAP model instances is of the same order as that for solving the CAP instances. This finding is important because chance constrained optimization models are very difficult to solve when the coefficients in the constraints are random.
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分布鲁棒联合机会约束分配问题的一种求解方法
我们研究了具有机会约束的分配问题(CAP)及其分布鲁棒对应的DR-CAP。我们提出了一种在这样一个公式中估计big-M的技术,该公式利用了模糊集。我们考虑了一个0-1双线性背包集来发展CAP和DR-CAP的有效不等式。这被推广到联合机会约束问题。还开发了一个概率切割框架来解决DR-CAP问题。对使用真实医院手术数据获得的问题实例的计算研究表明,所开发的技术使我们能够解决某些模型实例,并减少其他模型实例的计算时间。在DR-CAP模型中使用Wasserstein模糊集比通过增加样本平均近似技术中的样本大小可能的方法更显著地提高了满足机会约束的样本外性能。DR-CAP模型实例的解决时间与CAP实例的解决顺序相同。这一发现很重要,因为当约束中的系数是随机的时,机会约束优化模型很难求解。
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