Two-stage recoverable robust optimization for an integrated location–allocation and evacuation planning problem

We consider an integrated location–allocation and evacuation planning problem in a disaster context, where the effects of a disaster, including the uncertain capacities of relief facilities (rescue centers and distribution centers), uncertain demands for relief supplies and casualty treatment services, and uncertain availability of transportation links are characterized by a discrete scenario set. Instead of complete failures, we allow the disrupted relief facilities only lose part of their capacity. To deal with the uncertainties, we propose a two-stage recoverable robust optimization model, where the location decision of relief facilities, the allocation decision of delivering relief supplies from relief facilities to affected areas, the transfer decision of transporting casualties from affected areas to rescue centers etc are defined in two stages where the first-stage solution should be robust against the possible effects of a disaster that are revealed in the second stage, and the second-stage solution involves some recovery actions, which we term as multi-mitigation strategies: re-opening and re-operation, re-allocation, and relief supply sharing, to mitigate the effects. To solve the model to optimality, we develop a nested two-stage decomposition algorithm that iterates between a master problem considering only a subset of disaster scenarios solved by a Benders decomposition algorithm that incorporates some non-trivial acceleration strategies, and an adversarial separation problem that identifies disaster scenarios to enhance the worst-case recovery cost of the master problem. We introduce some warm-start techniques to accelerate the convergence of the solution algorithm. We conduct numerical studies on simulation instances to assess the performance of the solution algorithm, and analyze the robustness and recoverability of the model. We also conduct extensive numerical studies on realistic instances from Ya'an and Ganzi to demonstrate the benefits of accounting for recoverable robustness over a stochastic policy and a robust policy without recovery actions, the benefits of considering integrated optimization over sequential optimization, and the benefits of considering partial capacity loss and multi-mitigation strategies.