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

2026-04-24

AI Summary

This study addresses the challenges of limited battery energy and time-window conflicts in truck-drone collaborative last-mile delivery by introducing the first systematic formulation of the drone parcel assignment problem that incorporates the placement of charging/swapping stations. The authors propose an optimization model with explicit energy budget constraints and develop a polynomial-time approximation algorithm based on the First-Fit Decreasing (FFD) bin-packing strategy, integrated with interval scheduling and resource constraints. The algorithm achieves approximation ratios of (2+ψ), (4+ψ), and an improved (3+ψ) across different scenarios, where ψ is a function of the battery budget and extreme delivery costs. Experimental results demonstrate that the proposed approach consistently yields near-optimal solutions across diverse instances, offering strong practical utility while maintaining rigorous theoretical performance guarantees.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Combinatorial Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Economics, Online Markets and Human Computation: The sharing economy

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 $(2+ ψ)$-approximation algorithm. In the presence of both battery stations and conflicting intervals, we present a $(4+ψ)$-approximation algorithm. The algorithm is later modified into a $(3+ψ)$-approximation algorithm when the battery service stations act as swapping stations. Here $ψ$ 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.

Problem

• Drone Delivery
• Energy Constraint
• Last-Mile Logistics
• Packing Problem
• Battery Stations

Innovation

• Drone-Delivery Packing Problem
• Approximation Algorithms
• Battery Swapping Stations
• Last-Mile Logistics
• Energy-Constrained Scheduling