Two-stage distributionally robust programming based on worst-case mean-CVaR criterion and application to disaster relief management

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.