Optimizing last-mile delivery services: a robust truck-drone cooperation model and hybrid metaheuristic algorithm

In response to the increasing demand for faster customer service and cost-effective solutions in competitive markets, many companies are exploring strategies and tools to streamline their services. One emerging approach involves the integration of drones with trucks, offering potential benefits such as reduced environmental impact and delivery time. This study focuses on the use of a single truck coordinating with multiple drones for postal package delivery. The drones are transported by the truck, and both vehicles are responsible for carrying out deliveries. To account for weather uncertainties, specifically wind direction and speed affecting drone travel time, a robust optimization model is developed to address the truck-drone routing problem. Additionally, a hybrid metaheuristic algorithm is proposed, combining Adaptive Large Neighborhood Search, Clarke and Wright Saving Algorithm, and Genetic Algorithm. The effectiveness of this algorithm is assessed through numerical experiments, including sensitivity analyses on key problem parameters. The findings demonstrate that the proposed model has practical applications in last-mile delivery services, while the algorithm provides near-optimal solutions within a reasonable timeframe (ALNS reaches the solutions 3500% faster than GAMS for small-sized problems in average). Also the results show that with the 100% increase in average distance between nodes in the network, the service time increases by more than 200%.