Distributionally robust multi-period location-allocation with multiple resources and capacity levels in humanitarian logistics

Humanitarian logistics often faces the challenge of dealing with uncertainties when developing a rescue strategy in response to the occurrence of a disaster. We develop a distributionally robust model (DRM) for the multi-period location-allocation problem with multiple resources and capacity levels under uncertain emergency demand and resource fulfilment time with only limited distributional information being available in humanitarian logistics. We show that the model can be equivalently reformulated as a mixed-integer linear program, and develop a tailored branch-and-Benders-cut algorithm to solve it. To enhance the efficiency of the algorithm, we propose some improvement strategies, including in-out Benders cut generation, dual lifting, and normalization of the dual variables. We perform extensive numerical studies to verify the performance of the developed algorithm, assess the value of the DRM over the corresponding deterministic and stochastic models, and discuss the impacts of key model parameters to gain managerial insights, particularly for the decision-maker planning on allocating resources based on tradeoff among the operating cost, equity and efficiency. We also demonstrate how our model performs had it been used in the actual earthquake that occurred in Jiuzhaigou, China.