Given a fleet of drones with different speeds and a set of package delivery requests, the collaborative delivery problem asks for a schedule for the drones to collaboratively carry out all package deliveries, with the objective of minimizing the total travel time of all drones. We show that the best non-preemptive schedule (where a package that is picked up at its source is immediately delivered to its destination by one drone) is within a factor of three of the best preemptive schedule (where several drones can participate in the delivery of a single package). Then, we present a constant-factor approximation algorithm for the problem of computing the best non-preemptive schedule. The algorithm reduces the problem to a tree combination problem and uses a primal-dual approach to solve the latter. We have implemented a version of the algorithm optimized for practical efficiency and report the results of experiments on large-scale instances with synthetic and real-world data, demonstrating that our algorithm is scalable and delivers schedules of excellent quality.

翻译：给定一组具有不同速度的无人机机队及一系列包裹配送请求，协同配送问题要求为无人机制定调度方案，使其能协作完成所有包裹配送，目标是最小化所有无人机的总行程时间。我们证明，最优非抢占式调度（即包裹在起点被拾取后立即由单一无人机运抵目的地）的效能与最优抢占式调度（允许多架无人机参与单个包裹的配送）相比，其近似比不超过三倍。随后，我们提出一种常数倍近似算法，用于计算最优非抢占式调度方案。该算法将原问题归约为树组合问题，并采用原始对偶方法求解后者。我们实现了针对实际效率优化的算法版本，并报告了基于合成数据与真实数据的大规模实例实验结果，表明所提算法具有良好的可扩展性，并能生成高质量的调度方案。