During recent years, several companies have introduced small autonomous delivery robots and evidenced their technical applicability in field studies. However, a holistic planning framework for routing and utilizing these robots is still lacking. Current literature focuses mainly on logistical performance of delivery using autonomous robots, ignoring real world limitations, and does not assess the respective impact on total delivery costs. In contrast, this paper presents an approach to cost-optimal routing of a truck-and-robot system for last-mile deliveries with time windows, showing how to minimize the total costs of a delivery tour for a given number of available robots. Our solution algorithm is based on a combination of a neighborhood search with cost-specific priority rules and search operators for the truck routing, while we provide and evaluate two alternatives to solve the robot scheduling subproblem: an exact and a heuristic approach. We show in numerical experiments that our approach is able to reduce last-mile delivery costs significantly. Within a case study, the truck-and-robot concept reduces last-mile costs by up to 68% compared to truck-only delivery. Finally, we apply sensitivity analyses to provide managerial guidance on when truck-and-robot deliveries can efficiently be used in the delivery industry.

中文翻译：

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最后一英里交付的成本最优卡车和机器人路线

近年来，几家公司推出了小型自主送货机器人，并证明了它们在现场研究中的技术适用性。然而，仍然缺乏用于路由和利用这些机器人的整体规划框架。目前的文献主要关注使用自主机器人交付的物流性能，忽略现实世界的限制，并且没有评估各自对总交付成本的影响。相比之下，本文提出了一种卡车和机器人系统的成本优化路由方法，用于具有时间窗的最后一英里交付，展示了如何最小化给定数量的可用机器人的交付之旅的总成本。我们的解决方案算法基于邻域搜索与特定成本优先规则和卡车路线搜索运算符的组合，同时我们提供并评估了两种解决机器人调度子问题的替代方案：精确方法和启发式方法。我们在数值实验中表明，我们的方法能够显着降低最后一英里的交付成本。在一个案例研究中，与仅卡车交付相比，卡车和机器人概念将最后一英里的成本降低了 68%。最后，我们应用敏感性分析来为卡车和机器人交付何时可以有效地用于交付行业提供管理指导。