Work

The two-tier multi-depot vehicle routing problem with robot stations and time windows

Year: 2025

Type: article

Abstract: The deployment of self-driving or autonomous robots in last-mile logistics can significantly reduce traffic congestion and operational costs. Delivery systems that split the distribution process into two layers, with trucks in the first layer and autonomous robots at robot stations in the second layer, are known as Two-Tier Vehicle Routing Problems with Robot Stations (2T-VRP-RS). This paper extends the 2T-VRP-RS to include multiple depots supplying robot stations with parcels, which then deploy robots to serve customers within their time windows (2T-MDVRP-RS-TW). To solve the 2T-MDVRP-RS-TW, we propose a Mixed-Integer Linear Programming (MILP) formulation and develop a Multi-Start Iterated Local Search metaheuristic with Crossover and Repair (MS-ILS-CR) operators. Our approach integrates three strategies: (i) a Multi-Start mechanism, (ii) a Crossover operator, and (iii) a Repair operator from Variable Neighborhood Search, Genetic Algorithm, and Adaptive Large Neighborhood Search metaheuristics, respectively. We introduce a new instance set for comparison and validation, providing decision-makers with insights into the 2T-MVRP-RS-TW. Results show that the exact method is competitive only for small instances, while our metaheuristic approach outperforms the MILP model in both solution quality and computational times for small instances. Additionally, the multi-start, crossover, and repair operators in the MS-ILS-CR improve performance over similar metaheuristic approaches. The findings indicate that the 2T-MDVRP-RS has limited sensitivity to time-window widths but significant sensitivity to the number and location of depots.

Source: Engineering Applications of Artificial Intelligence

DOI: 10.1016/j.engappai.2025.110258

Authors: Giovanni Campuzano, Eduardo Lalla-Ruiz, Martijn Mes

Institutions: San Sebastián University, University of Twente

Language: English

Topic: Vehicle Routing Optimization Methods

Subfield: Industrial and Manufacturing Engineering

Field: Engineering

Domain: Physical Sciences

SDGs: Industry, innovation and infrastructure, Sustainable cities and communities

Open Access status: hybrid

Estimated APC paid: $3,200