Minimizing Total Travel Time for Collaborative Package Delivery with Heterogeneous Drones

TL;DR

This paper addresses optimizing drone schedules for package delivery to minimize total travel time, introducing a constant-factor approximation algorithm and demonstrating its scalability and effectiveness through experiments.

Contribution

It presents the first constant-factor approximation algorithm for non-preemptive drone delivery scheduling with heterogeneous speeds.

Findings

Algorithm achieves near-optimal schedules in large-scale tests

Proves non-preemptive schedules are within a factor of three of preemptive ones

Experimental results show high-quality, scalable solutions

Abstract

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.