Two-echelon electric vehicle routing problem incorporating robots for last-mile delivery

In response to the increasing demand for door-to-door services and the complexities of modern last-mile delivery models, this study investigates a two-echelon vehicle routing problem for last-mile delivery based on a multi-fleet framework. This framework includes electric vehicles (EVs) to transport robots and cargo, delivery robots (DRs) for terminal deliveries, and vans to recover robots, which is also referred to as an EV-DR-van system. We propose a mathematical model to address the two-echelon electric vehicle routing problem, considering time window constraints, the utilization of delivery robots, and a partial charging strategy, named 2E-EVRPTWDR-PC. We employ the CPLEX solver to obtain optimal solutions for small-scale instances. For larger instances, we design an adaptive large-neighborhood search algorithm (ALNS) to effectively explore and adapt to the complex solution space, producing high-quality results. The data for this research are generated by modifying Solomon’s dataset. Our experimental results confirm the proposed model’s validity and the algorithm’s effectiveness. Comparative analyses indicate that using robots for final deliveries can reduce overall time costs by approximately 20% compared to traditional delivery methods. This research has significant implications for optimizing last-mile delivery systems and improving delivery efficiency.