Coordinating road recovery and supply distribution in emergency services: A distributionally robust optimisation approach

When a disaster strikes, the connectivity of the road network is often severely compromised, hindering the distribution of relief supplies. Poor coordination in such scenarios not only wastes limited rescue resources, but also exacerbates the crisis, leading to greater harm to the affected population. As a result, scheduling of road recovery and supply distribution is deeply interdependent and requires thorough planning before initiating rescue missions. In this study, we address this planning-level optimisation problem involving road recovery and relief distribution under uncertainties to minimise both the distribution time and the shortage of relief supplies. Given the limited information on supply demand and recovery capability post-disaster, and potential changes in road network connectivity, a distributionally robust optimisation (DRO) model is developed and the ε-constraint method is then adopted to convert the DRO model into two subproblems. The first subproblem plans the scheduling and routing of repair crews considering possible changes on the road network connectivity, and then derives the corresponding plans for distribution fleets. The second subproblem further determines the allocation of relief supplies. A computationally tractable reformulation of the proposed model is derived and a math-heuristic approach that combines adaptive large neighbourhood search (ALNS) with a commercial solver is developed. Extensive experiments validate the robustness of the DRO approach, the superiority of integrated optimisation, the trade-off between objectives, and the diminishing returns of additional rescue resources.