Globalised robust bilevel model for multi-commodity distribution and vehicle assignment in post-disaster rescue

Post-disaster rescue is the process of managing a series of actions such as commodity distribution and vehicle assignment, to alleviate the suffering of affected people and losses. However, finding the optimal strategy for post-disaster rescue is challenging due to the complexity arising from the hierarchical relationship and uncertainty. A bilevel globalised robust optimisation (GRO) model is built to formulate this joint multi-commodity distribution and vehicle assignment problem. The GRO method is adapted to find the robust solution for all uncertain parameter values by controlling the distance of the parameter from the normal perturbation set. The upper and lower level objectives, which reflect fairness and timeliness, are to minimise the unsatisfied demand and transportation time, respectively. We derive a tractable GRO model and employ Karush-Kuhn-Tucker (KKT) conditions to reformulate the initial model as a single level one solved by CPLEX software. The application of the model is illustrated by a case study of a tornado. Computational results indicate that bilevel optimisation achieves a balance between fair distribution and timely response, and the GRO method can effectively resist uncertainty. Our optimisation approach is beneficial for managers to make efficient decisions in rescue activities.