Abstract In recent years, drone routing and scheduling has become a highly active area of research. This research introduces a new routing model that considers a synchronized truck-drone operation by allowing multiple drones to fly from a truck, serve one or multiple customers, and return to the same truck for a battery swap and package retrieval. The model addresses two levels (echelons) of delivery: primary truck routing from the main depot to serve assigned customers and secondary drone routing from the truck, which behaves like a moveable intermediate depot to serve other sets of customers. The model takes into account both trucks' and drones’ capacities with the objective of finding optimal routes of both trucks and drones that minimizes the total arrival time of both trucks and drones at the depot after completing the deliveries. The problem can be solved by formulated mixed integer programming (MIP) for the small-size problem, and two efficient heuristic algorithms are designed to solve the large-size problems: Drone Truck Route Construction (DTRC) and Large Neighborhood Search (LNS). Numeric results from the experiment compare the performance of both heuristics against the MIP method in small/medium-size instances from the literature. A sensitivity analysis is conducted to show the delivery time improvement of the proposed model over the previous truck-drone routing models.

中文翻译：

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无人机最后一公里配送的两梯队车辆路径问题

摘要 近年来，无人机路由和调度已成为一个非常活跃的研究领域。这项研究引入了一种新的路线模型，该模型考虑了同步卡车无人机操作，允许多架无人机从一辆卡车上飞行，为一个或多个客户提供服务，然后返回同一辆卡车进行电池更换和包裹检索。该模型解决了两个级别（梯队）的交付问题：从主要仓库为指定客户提供服务的主要卡车路线和从卡车出发的辅助无人机路线，其行为就像一个可移动的中间仓库，为其他客户群提供服务。该模型同时考虑了卡车和无人机的容量，目的是找到卡车和无人机的最佳路线，最大限度地减少卡车和无人机在完成交付后到达仓库的总时间。该问题可以通过为小规模问题制定的混合整数规划（MIP）来解决，并且设计了两种有效的启发式算法来解决大规模问题：无人机卡车路线构建（DTRC）和大型邻域搜索（LNS）。实验的数值结果在文献中的中小型实例中比较了两种启发式算法与 MIP 方法的性能。进行敏感性分析以显示所提出的模型相对于以前的卡车-无人机路线模型的交付时间改进。实验的数值结果在文献中的中小型实例中比较了两种启发式算法与 MIP 方法的性能。进行敏感性分析以显示所提出的模型相对于以前的卡车-无人机路线模型的交付时间改进。实验的数值结果在文献中的中小型实例中比较了两种启发式算法与 MIP 方法的性能。进行敏感性分析以显示所提出的模型相对于以前的卡车-无人机路线模型的交付时间改进。