Abstract The crew scheduling and routing problem (CSRP) consists of determining the best route and schedule for a single crew to repair damaged nodes in a network affected by extreme events. The problem also involves the design of paths to connect a depot to demand nodes that become accessible only after the damaged nodes in these paths are repaired. The objective is to minimize the total time that demand nodes remain inaccessible from the depot. The integrated scheduling and routing decisions make the problem too complicated to be effectively solved using mixed-integer programming (MIP) formulations. In this paper, we propose exact, heuristic and hybrid approaches for the CSRP. Specifically, we introduce (i) a branch-and-Benders-cut (BBC) method that enhances a previous approach by using a different variable partitioning scheme and new valid inequalities that strengthen the linear relaxation of the master problem; (ii) genetic algorithm and simulated annealing metaheuristics; and (iii) an exact hybrid BBC (HBBC) method that effectively combines the first two approaches. Computational experiments using benchmark instances show that the proposed algorithms can solve large-scale instances in comparison to other methods proposed in the literature, mainly as result of the enhanced BBC method and the hybridization scheme. The HBBC method obtained feasible solutions for the 390 tested instances, solving 30 of them to proven optimality for the first time. On average, it improved the best known lower and upper bounds by 15.21% and 8.41%, respectively, and reduced the computational times by more than 70% with respect to the standalone BBC.

中文翻译：

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道路修复中人员调度和路由问题的分解算法

摘要 机组调度和路由问题（CSRP）包括确定单个机组修复受极端事件影响的网络中损坏节点的最佳路由和调度。该问题还涉及将站点连接到需求节点的路径设计，这些节点只有在修复这些路径中的损坏节点后才能访问。目标是最大限度地减少需求节点无法从仓库访问的总时间。集成的调度和路由决策使问题过于复杂，无法使用混合整数规划 (MIP) 公式有效解决。在本文中，我们为 CSRP 提出了精确的、启发式的和混合的方法。具体来说，我们引入了 (i) 一种分支和弯曲切割 (BBC) 方法，该方法通过使用不同的变量分区方案和新的有效不等式来增强主问题的线性松弛，从而增强了以前的方法；(ii) 遗传算法和模拟退火元启发式；(iii) 一种有效结合前两种方法的精确混合 BBC (HBBC) 方法。使用基准实例的计算实验表明，与文献中提出的其他方法相比，所提出的算法可以解决大规模实例，这主要是增强的 BBC 方法和杂交方案的结果。HBBC 方法为 390 个测试实例获得了可行解，首次解决了其中的 30 个以证明最优性。平均而言，它将最著名的下限和上限提高了 15.21% 和 8.41%，