Hybrid risk-averse location-inventory-allocation with secondary disaster considerations in disaster relief logistics: A distributionally robust approach

This paper addresses facility location, inventory pre-positioning and allocation of emergency supplies in disaster relief logistics by taking into account both primary and secondary disasters. To characterize the uncertainty associated with post-disaster demand and resource allocation cost, this paper constructs the statistical-distance-based ambiguity sets of possible probability distributions with the Wasserstein metric, which is utilized to measure their distances from the empirical distribution. Armed with the Wasserstein ambiguity set, this paper develops a hybrid risk-averse three-stage distributionally robust chance-constrained (TS-DRCC) model for the considered problem, which measures the risk from both quantitative and qualitative aspects. When the Wasserstein metric uses the l1-norm, this paper reformulates the proposed TS-DRCC model as a mixed-integer linear program (MILP) based on the strong duality theory, which can be efficiently solved via CPLEX, thereby enabling decision-makers to use it. Theoretically, this paper also proves that the proposed TS-DRCC model converges to stochastic programming (SP) model as the size of historical data approaches infinity. Finally, this paper conducts a computational study of hurricane threat in the US to indicate the superiority of our proposed TS-DRCC model in terms of demand satisfaction and out-of-sample performance compared to the model considering only primary disasters and the conventional SP model, respectively. Some key managerial insights are summarized as rules of thumb to effectively guide the integrated pre- and post-disaster relief actions in the disaster relief logistics planning practice.