Approximation algorithms for drone delivery scheduling with a fixed number of drones

The coordination among drones and ground vehicles for last-mile delivery has gained significant interest in recent years. In this paper, we study multiple drone delivery scheduling problem (MDSP) [1] 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 single drone delivery scheduling problem (SDSP). Also, we propose two approximation algorithms of factor 1/3 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 1/6 rho-approximation algorithm, where rho is the ratio between the minimum and maximum battery capacity of the drones.