This work addresses an operational problem of a logistics service provider that consists of finding an optimal route for a vehicle carrying customer parcels from a central depot to selected facilities, from where autonomous devices like robots are launched to perform last-mile deliveries. The objective is to minimize a tardiness indicator based on the customer delivery deadlines. This article provides a better understanding of how three major tardiness indicators can be used to improve the quality of service by minimizing the maximum tardiness, the total tardiness, or the number of late deliveries. We study the problem complexity, devise a unifying Mixed Integer Programming formulation and propose an efficient branch-and-Benders-cut scheme to deal with instances of realistic size. Numerical results show that this novel Benders approach with a tailored combinatorial algorithm for generating Benders cuts largely outperforms all other alternatives. In our managerial study, we vary the number of available facilities, the coverage radius of autonomous robots and their speed, to assess their impact on the quality of service and environmental costs.

这项工作解决了物流服务提供商的运营问题，该问题包括为运送客户包裹的车辆从中央仓库到选定设施寻找最佳路线，从那里启动机器人等自主设备以执行最后一英里的交付。目标是根据客户交付期限最小化迟到指标。本文提供了对如何使用三个主要迟到指标通过最小化最大迟到、总迟到或延迟交付次数来提高服务质量的更好理解。我们研究了问题的复杂性，设计了一个统一的混合整数规划公式，并提出了一种有效的分支和 Benders-cut 方案来处理实际大小的实例。数值结果表明，这种新颖的 Benders 方法与用于生成 Benders 削减的定制组合算法在很大程度上优于所有其他替代方案。在我们的管理研究中，我们改变了可用设施的数量、自主机器人的覆盖半径及其速度，以评估它们对服务质量和环境成本的影响。