Drones have been increasingly used for deliveries; however, delivering packages directly to customers is still challenging, particularly in densely populated urban areas. To overcome this, drone resupply has been proposed, where drones carry packages to trucks en route, and then trucks make the final deliveries. Existing studies have only considered the case of one truck and one drone. In this study, we investigate drone resupply with multiple trucks and drones for the on-time delivery of late-available packages. Considering practical operations in urban areas, we focus on a situation where trucks deliver packages along given routes. This raises the drone resupply scheduling problem, which aims to maximise the total value of the late-available packages that can be delivered on time. We formally define the problem and analyse its optimality properties. Then, we develop an exact solution approach based on a time-expanded network flow model and design a greedy heuristic algorithm. We validate the efficiency and effectiveness of the proposed solutions through computational studies. Operational insights and guidance are derived for the application of drones in on-time delivery.

中文翻译：

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无人机为多辆卡车和无人机补给，以便沿着给定的卡车路线准时交付


无人机越来越多地用于送货；然而，直接向客户递送包裹仍然具有挑战性，特别是在人口稠密的城市地区。为了克服这个问题，有人提出了无人机补给，即无人机将包裹运送到途中的卡车上，然后卡车进行最终的交付。现有的研究仅考虑了一辆卡车和一架无人机的情况。在这项研究中，我们研究了使用多辆卡车和无人机进行无人机补给，以按时交付迟到的包裹。考虑到城市地区的实际操作，我们关注的是卡车沿指定路线运送包裹的情况。这就提出了无人机补给调度问题，其目的是最大化可按时交付的迟到包裹的总价值。我们正式定义问题并分析其最优性属性。然后，我们开发了一种基于时间扩展网络流模型的精确求解方法，并设计了贪婪启发式算法。我们通过计算研究验证了所提出的解决方案的效率和有效性。为无人机在准时交付中的应用提供了操作见解和指导。