Distributionally robust location-allocation with demand and facility disruption uncertainties in emergency logistics

Emergency logistics is vital to disaster relief management. In this paper we develop a distributionally robust optimization model (DROM) for optimizing the locations of distribution centres and backup warehouses, and the distribution of disaster relief supplies in emergency logistic networks by minimizing the expected total cost and the total delivery time. Based on limited historical distribution information, the model considers uncertain demand and uncertain facility disruptions, and describes their distributions through ambiguity sets. Following the adaptability and tractability of the ambiguity sets, we show that the model can be equivalently re-formulated as a mixed-integer linear program. To solve the model, we propose an exact algorithm based on Benders decomposition (BD). We also introduce an in-out Benders cut generation strategy to improve the efficiency of the BD algorithm. Finally, we perform extensive numerical studies to test the performance of the BD algorithm, ascertain the benefits of the proposed DROM over the corresponding deterministic and stochastic models, and examine the impacts of the key model parameters to gain managerial insights.