Humanitarian transportation network design via two-stage distributionally robust optimization

Natural disasters are highly unpredictable, with varying degrees of magnitude, and thus require a reliable and robust humanitarian relief network. Faced with the adverse effects of disasters, we advocate taking pre-disaster preventive actions, e.g., road link strengthening, to mitigate post-disaster disruptions to road networks. In this paper, we study a highly integrated humanitarian relief network design problem, in which the network strengthening plan and inventory pre-positioning scheme are optimized cooperatively. The proposed problem is formulated as a two-stage distributionally robust optimization (DRO) model, in which the first and second stages correspond to pre- and post-disaster relief operations, respectively. By leveraging prior data and the Wasserstein metric, a tailored ambiguity set is constructed to capture both node- and link-wise uncertainties. We demonstrate that the two-stage DRO model over the Wasserstein ambiguity set has an equivalent reformulation that can be solved via the L-shaped method with bilinear subproblems. Based on observations of the problem structure and the spirit of separation optimization, both exact and heuristic approaches are proposed to address the bilinear subproblems. Via the case study of the Yushu earthquake, we highlight the value of jointly optimizing network strengthening and inventory pre-positioning decisions. Specifically, with the same investment budget, integrating network strengthening into inventory pre-positioning can easily achieve an approximately 60% reduction in shortage penalties. Furthermore, our method can produce reliable solutions, based on which we explore several managerial implications.