Abstract This paper introduces the Traveling Salesman Problem with Release Dates and Drone Resupply, which consists of finding a minimum time route for a single truck that can receive newly available orders en route via a drone sent from the depot. We assume that each order’s release date is known at the time of delivery planning. This context is common for many applications, notably last-mile logistics. We develop a Mixed-Integer Linear Program and a solution approach for larger instances based on decomposing the problem into the truck-routing and the drone-resupply decisions. Numerical experiments show that using drones for resupply can reduce the total delivery time by up to 20%. Additionally, experiments show that the decomposition can rapidly obtain high-quality solutions. For instances of 10 and 15 customers, the decomposition solved the majority to optimality, with a trivial gap. For larger instances, this approach provided lower delivery times than a traditional parcel delivery system using a truck only. Investigations on the effects of drone speed, drone capacity, depot location, constraint addition, and allowing the truck to return to the depot are studied. We consider instances up to 50 customers.

中文翻译：

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发布日期和无人机补给的旅行商问题

摘要 本文介绍了具有发布日期和无人机补给的旅行商问题，该问题包括为一辆卡车寻找最短时间路线，该卡车可以通过从仓库发送的无人机在途中接收新的可用订单。我们假设每个订单的发布日期在交付计划时是已知的。这种情况在许多应用中很常见，尤其是最后一英里物流。我们开发了一个混合整数线性程序和一个基于将问题分解为卡车路线和无人机再补给决策的大型实例的解决方案。数值实验表明，使用无人机进行补给可以将总交付时间缩短多达 20%。此外，实验表明分解可以快速获得高质量的解决方案。对于 10 个和 15 个客户的实例，分解解决了大多数优化问题，但有一个微不足道的差距。对于较大的实例，与仅使用卡车的传统包裹递送系统相比，这种方法提供的递送时间更短。研究了无人机速度、无人机容量、仓库位置、约束添加和允许卡车返回仓库的影响。我们考虑最多 50 个客户的实例。