The Multiple Drone-Delivery Scheduling Problem (MDSP) is a scheduling problem that optimizes the maximum reward earned by a set of $m$ drones executing a sequence of deliveries on a truck delivery route. The current best-known approximation algorithm for the problem is a $\frac{1}{4}$-approximation algorithm developed by Jana and Mandal (2022). In this paper, we propose exact and approximation algorithms for the general MDSP, as well as a unit-cost variant. We first propose a greedy algorithm which we show to be a $\frac{1}{3}$-approximation algorithm for the general MDSP problem formulation, provided the number of conflicting intervals is less than the number of drones. We then introduce a unit-cost variant of MDSP and we devise an exact dynamic programming algorithm that runs in polynomial time when the number of drones $m$ can be assumed to be a constant.

翻译：多无人机配送调度问题（MDSP）是一类调度优化问题，旨在最大化由$m$架无人机在卡车运输路线上执行一系列配送任务所获得的总收益。当前已知该问题的最佳近似算法是由Jana和Mandal（2022）提出的$\frac{1}{4}$-近似算法。本文针对一般MDSP问题及其单位成本变体，提出了精确算法与近似算法。首先，我们提出一种贪心算法，并证明当冲突区间数量少于无人机数量时，该算法对一般MDSP问题表述可达到$\frac{1}{3}$-近似比。随后，我们引入MDSP的单位成本变体，并设计了一种精确动态规划算法，当无人机数量$m$可视为常数时，该算法具有多项式时间复杂度。