In this paper, we simultaneously capture several practical features in disaster relief management: integrated facility location, inventory pre-positioning and delivery decisions, relief resource priority, partial probability information of demand and risk-averse criterion. We cast the problem as a two-stage distributionally robust mean-conditional value-at-risk (CVaR) optimization model, for which we derive computationally tractable counterparts under the box and polyhedral ambiguity sets. We further identify the relationship between the proposed distributionally robust model and the traditional two-stage stochastic programming model. We assess the performance of the proposed model by an illustrative small-sized example. From the out-of-sample analysis, we show the superiority of the distributionally robust model compared to the two-stage stochastic programming model in terms of stability. We also implement the proposed model in a realistic large-scale case study of hurricane threats in the southeastern US. We finally achieve the managerial implications and insights of using the distributionally robust optimization method.

在本文中，我们同时捕获了救灾管理中的一些实用功能：综合设施位置，库存预定位和交付决策，救灾资源优先级，需求的部分概率信息和规避风险的标准。我们将该问题转换为两阶段分布鲁棒均值条件风险值（CVaR）优化模型，针对该模型，我们得出了箱形和多面体歧义集下在计算上易于处理的对应项。我们进一步确定了所提出的分布鲁棒模型与传统的两阶段随机规划模型之间的关系。我们通过一个示例性的小型示例来评估所提出模型的性能。根据样本外分析，我们在稳定性方面显示了与两阶段随机规划模型相比，分布鲁棒模型的优越性。我们还在现实的美国东南部飓风威胁的大规模案例研究中实施了建议的模型。最后，我们获得了使用分布式鲁棒优化方法的管理意义和见解。