The demand for efficient last-mile delivery systems in large cities creates an opportunity to develop innovative logistics schemes. In this paper, we study a problem in which each vehicle may travel with more than one deliveryman to serve multiple customers with a single stop of the vehicle, increasing the delivery efficiency. We extend the vehicle routing problem with time windows and multiple deliverymen by explicitly considering the deliveryman routes. We introduce the problem, formally define it with a formulation, propose valid inequalities, and develop a tailored branch-and-Benders-cut (BBC) algorithm to solve it. The BBC is capable of solving 89% of the instances to proven optimality in reasonable times, many of them of realistic sizes. Additionally, we show the benefits of evaluating the deliveryman routes considering a cost minimization perspective, and discuss relevant solutions for urban logistics problems that can help decrease congestion and emissions.

中文翻译：

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多送货员最后一英里送货路线问题的精确方法

大城市对高效最后一英里交付系统的需求为开发创新物流方案创造了机会。在本文中，我们研究了一个问题，即每辆车可以搭载多个送货员，从而在车辆的一个停靠站为多个客户提供服务，从而提高送货效率。我们通过明确考虑送货员路线，将车辆路径问题扩展到时间窗和多个送货员。我们引入问题，用公式正式定义它，提出有效的不等式，并开发定制的分支和本德斯切割（BBC）算法来解决它。 BBC 能够在合理的时间内解决 89% 的实例，以证明其最优性，其中许多实例的规模都非常实际。此外，我们还展示了从成本最小化角度评估送货员路线的好处，并讨论了有助于减少拥堵和排放的城市物流问题的相关解决方案。