The traveling salesman problem is one of the most studied problems in combinatorial optimization. An emerging variant of this problem, which is referred to as the traveling salesman problem with drone, focuses on deploying a drone and a delivery truck for last-mile delivery. This problem coordinates the truck and drone deliveries in both time and location because the drone requires the truck to refresh its battery and load the next customer’s package on the drone. Previous studies assume that the drone battery is swapped with a new/fully recharged battery at the end of each drone flight. In contrast, this study investigates a flexible recharging policy. For this purpose, we develop a new mixed integer linear programming formulation into which remaining battery level consideration is incorporated. A computational study is provided to compare the recharging policy with the battery swapping policy in terms of delivery time. Due to the complexity of the problem, a heuristic approach is proposed to solve medium-sized instances.

旅行商问题是组合优化中研究最多的问题之一。这个问题的一个新变种，被称为无人机的旅行商问题，专注于部署无人机和送货卡车进行最后一英里的交付。这个问题在时间和位置上协调卡车和无人机的交付，因为无人机需要卡车更新电池并将下一个客户的包裹装载到无人机上。以前的研究假设无人机电池在每次无人机飞行结束时更换为新的/充满电的电池。相比之下，本研究调查了灵活的充电政策。为此，我们开发了一种新的混合整数线性规划公式，其中考虑了剩余电池电量。提供了一项计算研究，以在交付时间方面比较充电策略与电池交换策略。由于问题的复杂性，提出了一种启发式方法来解决中等规模的实例。