Approximating Energy-Constrained Drone Delivery Packing Problem for Last-Mile Logistics

TL;DR

This paper introduces approximation algorithms for the Drone-Delivery Packing Problem, optimizing last-mile logistics by efficiently assigning parcels to drones with battery constraints in various scenarios.

Contribution

It presents novel approximation algorithms for three variants of the NP-hard problem, including cases with and without battery stations and conflicting delivery intervals.

Findings

Constant factor approximation for no battery stations case.

$(2+ \, \psi)$-approximation for non-conflicting intervals.

$(4+ \, \psi)$-approximation with battery stations and conflicts.

Abstract

Collaboration between drones and trucks in a last-mile delivery system offers numerous benefits and reduces many challenges of the traditional delivery system. Here, we introduce Drone-Delivery Packing Problem, where a set of parcels, associated with delivery intervals and cost, should be delivered to customer locations. The system comprises a set of identical drones and battery stations along truck's route, where drones swap depleted batteries or recharge them. The objective is to find assignment for all parcels by using the minimum number of drones, subject to the battery budget and compatibility of each drone's assignment. We consider three variants of the problem, based on conflicting characteristics and existence of battery service stations. All are NP-hard, and we have proposed approximation algorithms for each. When there are no battery stations, we propose a constant factor approximation algorithm using first fit decreasing bin packing algorithm. When the intervals are non-conflicting, we design a $(2+ \psi)$-approximation algorithm. In the presence of both battery stations and conflicting intervals, we present a $(4+\psi)$-approximation algorithm. The algorithm is later modified into a $(3+\psi)$-approximation algorithm when the battery service stations act as swapping stations. Here $\psi$ is a function of battery budget, minimum and maximum cost of the deliveries. Finally, we validate our results and compare the performance with the optimum on different instances.