Distributionally robust chance-constrained programming for multi-period emergency resource allocation and vehicle routing in disaster response operations

Emergency resource allocation and vehicle routing are the most essential and inseparable response actions in emergency management after disasters. In particular, disaster response operations are significantly affected by high uncertainty and incomplete dynamic information of demand and risk. For this purpose, we construct a risk-based ambiguity set for modeling the distributional uncertainty in the demand and describing the coupling relationship between the demand and risk in different periods (e.g., secondary disasters strike). Against this background, we present two distributionally robust chance-constrained programming (DRCCP) models with both individual and joint chance constraints for multi-period emergency resource allocation and vehicle routing problem under demand distributional ambiguity. For DRCCP with individual chance constraint, we can derive the computationally tractable reformulation of the proposed model with a safe approximation index. For DRCCP with joint chance constraint, we can use Bonferroni’s approximation to obtain a set of tractable individual chance constraints. As for the solution method, we first decompose the original model into the emergency resource allocation and vehicle routing subproblems, and then develop an efficient adaptive large neighborhood search (ALNS) algorithm. We evaluate the performance of the proposed ALNS heuristic algorithm on a hypothetical instance set and show that the ALNS algorithm is capable of producing high-quality solutions within a reasonable computing time. We also conduct a real case study of the Wenchuan earthquake in China to demonstrate the superiority of the proposed DRCCP approach in a comparative perspective. In addition, we provide some possible extensions of the considered problem. Finally, we explore the managerial insights that may be useful for the disaster response operation.