We address the problem of routing a fleet of trucks equipped with unmanned aerial vehicles, commonly known as drones, to perform deliveries in last-mile delivery process. The customers can be served by either a truck or a drone within the respective time window of each. Each capacitated truck carries drones that can be launched to perform deliveries. The drone takes off from a truck located either at a customer or at the depot and it must land on the same truck after visiting a customer to be served. The aim is to serve all customers at minimum cost, under time window, capacity, and flying endurance constraints. We formulate the problem as a mixed integer linear program (MILP) and develop a heuristic procedure where a two-phase strategy is embedded in a multi-start framework. The computational results are carried out on instances generated by starting from vehicle routing problem with time windows benchmarks. We analyze the behavior of the considered transportation system by mean of the solutions provided by the MILP. The proposed formulation is able to solve instances with up to 15 customers. The solutions of the MILP are used as benchmark to assess the effectiveness of the proposed heuristic procedure.

中文翻译：

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卡车和无人机在最后一英里交付过程中的合作

我们解决了为配备无人驾驶飞行器（通常称为无人机）的卡车车队安排路线以在最后一英里交付过程中执行交付的问题。客户可以在各自的时间窗口内由卡车或无人机提供服务。每辆有能力的卡车都装有无人机，可以发射无人机来执行交付。无人机从位于客户或仓库的卡车上起飞，并且必须在拜访客户后降落在同一辆卡车上才能得到服务。目标是在时间窗口、容量和飞行耐力限制下，以最低成本为所有客户提供服务。我们将问题表述为混合整数线性程序 (MILP)，并开发了一种启发式程序，其中将两阶段策略嵌入到多开始框架中。计算结果是在从车辆路径问题开始和时间窗口基准生成的实例上进行的。我们通过 MILP 提供的解决方案来分析所考虑的交通系统的行为。提议的公式能够解决多达 15 个客户的实例。MILP 的解决方案被用作基准来评估所提出的启发式程序的有效性。