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.

中文翻译：

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集成位置分配和疏散规划问题的两阶段可恢复鲁棒优化

我们考虑灾害背景下的综合位置分配和疏散规划问题，其中灾害的影响包括救援设施（救援中心和配送中心）的不确定能力、对救援物资和伤员治疗服务的不确定需求以及不确定性。交通连接的可用性由离散的场景集来表征。我们不会让受干扰的救援设施完全失效，而只是使其失去部分能力。为了应对不确定性，我们提出了一个两阶段可恢复鲁棒优化模型，其中包括救援设施的位置决策、救援设施向灾区运送救援物资的分配决策、将伤员从灾区运送至救援的转移决策。中心等被定义为两个阶段，第一阶段的解决方案应该能够抵御第二阶段中揭示的灾难可能产生的影响，第二阶段的解决方案涉及一些恢复行动，我们称之为多重缓解策略：重新开放和重新运营、重新分配和救援供应共享，以减轻影响。为了解决模型的最优问题，我们开发了一种嵌套的两阶段分解算法，该算法在仅考虑灾难场景子集的主问题和一个对抗性分离问题之间进行迭代，该主问题由 Benders 分解算法解决，该算法结合了一些重要的加速策略识别灾难场景，以提高主问题的最坏情况恢复成本。我们引入了一些热启动技术来加速求解算法的收敛。我们对模拟实例进行数值研究，以评估求解算法的性能，并分析模型的鲁棒性和可恢复性。我们还对雅安和甘孜的实际实例进行了广泛的数值研究，以证明考虑可恢复稳健性相对于随机策略和无恢复操作的稳健策略的好处，考虑集成优化相对于顺序优化的好处，以及考虑可恢复稳健性的好处。考虑部分容量损失和多重缓解策略。