We investigate a new exact solution approach for the Active Passive Vehicle Routing Problem, a vehicle routing problem with complicated temporal synchronisation requirements between vehicles. A key contribution is the introduction of a new principle, , for Benders Decomposition to produce disaggregated optimality cuts when traditional block-diagonality fails. The technique is applied to a new Mixed Integer Programming formulation of the Active Passive Vehicle Routing Problem. The formulation is built on coupled movements between active and passive vehicles, and solved using Combinatorial Benders Decomposition. The synchronisation constraints result in an interesting subproblem for which we present a tailored algorithm. The new method outperformed the existing Branch-and-Price method by two orders of magnitude and solves 74 instances to optimality for the first time. We investigate the performance impact of route enumeration, a heuristic and valid inequalities on the base Benders algorithm.

中文翻译：

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主动被动车辆路径问题的延迟分解 Benders 分解


我们研究了主动被动车辆路径问题的一种新的精确解决方法，这是一种车辆之间具有复杂时间同步要求的车辆路径问题。一个关键的贡献是引入了新原理 ，当传统的块对角性失败时，Benders 分解可以产生分类的最优性削减。该技术应用于主动被动车辆路径问题的新混合整数规划公式。该公式建立在主动和被动车辆之间的耦合运动的基础上，并使用组合弯曲器分解进行求解。同步约束导致了一个有趣的子问题，我们为此提出了一个定制的算法。新方法的性能比现有的 Branch-and-Price 方法高出两个数量级，并且首次解决了 74 个实例的最优问题。我们研究了路由枚举、启发式和有效不等式对基本 Benders 算法的性能影响。