Humanitarian relief logistics network design considering facility location, inventory pre-positioning and evacuation planning: A two-stage distributionally robust optimization approach

The high uncertainty in the occurrence, space, and scale of natural disasters presents significant challenges to reliable humanitarian relief logistics network (HRLN) design. After a disaster occurs, relief supplies and evacuees are usually transported simultaneously through the HRLN, which occupies limited logistics infrastructure (i.e., roads). This phenomenon drives the integration of three crucial decisions in the design of HRLNs: the emergency facility locations, the pre-positioning of the relief inventory, and the planning of human evacuation. This composite problem is formulated as a two-stage distributionally robust optimization model, with the two stages corresponding to pre-disaster and post-disaster decision-making. To capture the characteristics of the distribution functions of the number of evacuees and the road capacity, we design an ambiguity set using historical data and the type-1 Wasserstein metric. We show that there is an equivalent reformulation of the abovementioned model that can be solved by decomposition algorithms. Two versions of the decomposition algorithm, i.e., single-cut and multi-cut versions, are developed based on the generic Benders-decomposition technique. A case study is conducted on the Yushu earthquake in China and several managerial implications are proposed.