A combined Truck–drone system that delivers packages from a warehouse to multiple customers is investigated. The truck movements are restricted to the potential stops from which the drone with limited capacity takes off or lands. The aim is to determine both the best or ‘optimal’ sequence of the drone delivery trips and the best or ‘optimal’ trucks stops that will minimize the total combined truck drone delivery cost. This is an innovative delivery process which also falls under the umbrella of last mile delivery which is known to be one of the most challenging activities within logistics. The problem is first formulated as a 0–1 Linear programming model. A Variable Neighborhood Search (VNS) algorithm is then designed. The proposed metaheuristic is assessed on test problems from the online TSP library. A sensitivity analysis which examines the effect of a neighborhood removal, and the neighborhood sequencing is carried out. The metaheuristic has also shown to be reliable when tested against our mathematical model using the commercial optimizer CPLEX. Interesting overall results are discovered which demonstrate the robustness of the proposed VNS.

研究了一种卡车-无人机组合系统，该系统可将包裹从仓库运送到多个客户。卡车的移动仅限于容量有限的无人机起飞或降落的潜在停靠点。目的是确定无人机送货行程的最佳或“最佳”顺序以及最佳或“最佳”卡车停靠点，从而最大限度地降低卡车无人机送货的总成本。这是一种创新的交付流程，也属于最后一英里交付的范畴，众所周知，最后一英里交付是物流领域最具挑战性的活动之一。该问题首先被表述为 0-1 线性规划模型。然后设计了可变邻域搜索（VNS）算法。所提出的元启发式方法根据在线 TSP 库中的测试问题进行评估。进行敏感性分析，检查邻域移除的效果，并进行邻域排序。当使用商业优化器 CPLEX 对我们的数学模型进行测试时，元启发式方法也被证明是可靠的。有趣的总体结果被发现，证明了所提出的 VNS 的稳健性。