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

• Published in: Theoretical computer science Vol. 991; p. 114442
• Main Authors: Jana, Saswata, Mandal, Partha Sarathi
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 12.04.2024
• Subjects: Approximation algorithm; Complexity analysis; Drone delivery scheduling; Last-mile delivery system; Optimization; Drone delivery scheduling; Complexity analysis; Approximation algorithm; Optimization; Last-mile delivery system
• ISSN: 0304-3975
• DOI: 10.1016/j.tcs.2024.114442

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 13 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 16ρ-approximation algorithm, where ρ is the ratio between the minimum and maximum battery capacity of the drones. •An optimal pseudo-polynomial algorithm and FPTAS for the single drone delivery scheduling problem is proposed.•Two approximation algorithms for the multiple drone delivery scheduling problem are proposed.•An approximation algorithm for the multiple heterogeneous drone delivery scheduling problem is proposed.•We analyzed the approximation factors of all the aforementioned proposed algorithms and time complexities.