The coordination among drones and ground vehicles for last-mile delivery has gained significant interest in recent years. In this paper, we study (MDSP) for last-mile delivery, where we have a set of drones with an identical battery budget and a set of delivery locations; along with profit for delivery, cost, and delivery time intervals. The objective of the MDSP is to find conflict-free schedules for each drone such that the total profit gained is maximum subject to the battery constraint of the drones. This paper proposes an optimal pseudo-polynomial algorithm and a fully polynomial time approximation scheme (FPTAS) for the (SDSP). Also, we propose two approximation algorithms of factor for the MDSP with some constraints on the number of drones. We formulate the problem for the heterogeneous case, where the drones have non-identical battery capacities, and propose a -approximation algorithm, where is the ratio between the minimum and maximum battery capacity of the drones.

中文翻译：

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固定无人机数量的无人机配送调度近似算法

近年来，无人机和地面车辆之间最后一英里交付的协调引起了人们的极大兴趣。在本文中，我们研究了最后一英里交付的（MDSP），其中我们拥有一组具有相同电池预算和一组交付位置的无人机；以及交付利润、成本和交付时间间隔。MDSP 的目标是为每架无人机找到无冲突的时间表，以便在无人机电池限制的情况下获得最大利润。本文针对（SDSP）提出了一种最优伪多项式算法和一种完全多项式时间逼近方案（FPTAS）。此外，我们还提出了两种 MDSP 因子近似算法，并对无人机数量进行了一些限制。我们针对异构情况制定了问题，其中无人机具有不同的电池容量，并提出了一种近似算法，其中 是无人机的最小和最大电池容量之间的比率。