Risk-averse two-stage distributionally robust optimisation for logistics planning in disaster relief management

Relief logistics is vital to disaster relief management. Herein, a risk-averse two-stage distributionally robust programming model is proposed to provide decision support for planning disaster relief logistics. It is distinct from the conventional disaster relief logistics planning problem in that (i) the facility location-inventory model and the multi-commodity network flow formulation are integrated; (ii) the probability distribution information of the supply, demand, and road link capacity is partially known, and (iii) the two-stage distributionally robust optimisation (DRO) method based on the worst-case mean-conditional value-at-risk criterion is developed. For tractability, we reformulate the proposed DRO model as equivalent mixed-integer linear programs for box and polyhedral ambiguity sets, which can be directly solved to optimality using the CPLEX software. To evaluate the validity of the proposed DRO model, we conduct numerical experiments based on a real-world case study addressing hurricane threats in the Gulf of Mexico region of the United States. Furthermore, we compare the performance of the proposed DRO model with that of the conventional two-stage stochastic programming model. Finally, we report the managerial implications and insights of using the risk-averse two-stage DRO approach for disaster relief management.