Adopting unmanned aerial vehicles (UAV), also known as drones, into the last-mile-delivery sector and having them work alongside trucks with the aim of improving service quality and reducing the transportation cost gives rise to a new class of Vehicle Routing Problems (VRPs). In this paper, we introduce a new optimization problem called the min-cost Parallel Drone Scheduling Vehicle Routing Problem (PDSVRP). This problem is a variant of the well-known Parallel Drone Scheduling Traveling Salesman Problem (PDSTSP) recently introduced in the literature in which we allow multiple trucks and consider the objective of minimizing the total transportation costs. We formulate the problem as a Mixed Integer Linear Program and then develop a Ruin and Recreate ($\mathcal{R}\&\mathcal{R}$) algorithm. Exploiting PDSVRP solution characteristics in an effective manner, our heuristic manages to introduce “sufficient” rooms to a solution via new removal operators during the ruin phase. It is expected to enhance the possibilities for improving solutions later in the recreate phase. Multiple experiments on a new set of randomly generated instances confirm the performance of our approach. To explore the benefits of drone delivery as well as the insight into the impact of related factors on the contribution of drones’ use to operational cost, a sensitivity analysis is conducted. We also adapt the proposed algorithm to solve the PDSTSP and validate it via benchmarks available in the literature. It is shown that our algorithm outperforms state-of-the-art algorithms in terms of solution quality. Out of 90 considered instances, it finds 26 new best known solutions.

采用无人机（UAV），也称为无人机，进入最后一英里交付领域，并让它们与卡车一起工作，以提高服务质量和降低运输成本，从而引发了一类新的车辆路线问题（ VRP）。在本文中，我们介绍了一个新的优化问题，称为最小成本并行无人机调度车辆路由问题（PDSVRP）。这个问题是最近在文献中引入的著名的并行无人机调度旅行商问题（PDSTSP）的变体，其中我们允许多辆卡车并考虑最小化总运输成本的目标。我们将问题表述为一个混合整数线性规划，然后开发一个 Ruin and Recreate ($\mathcal{R}\&\mathcal{R}$） 算法。以有效的方式利用 PDSVRP 解决方案的特征，我们的启发式方法设法在破坏阶段通过新的移除操作员将“足够”的房间引入解决方案。预计将增加在重新创建阶段后期改进解决方案的可能性。对一组新的随机生成实例进行的多次实验证实了我们方法的性能。为了探索无人机交付的好处以及洞察相关因素对无人机使用对运营成本的贡献的影响，进行了敏感性分析。我们还调整了所提出的算法来解决 PDSTSP，并通过文献中可用的基准对其进行验证。结果表明，我们的算法在解决方案质量方面优于最先进的算法。在 90 个考虑的实例中，