The multi-visit vehicle routing problem with multiple heterogeneous drones

The integration of drones into last-mile delivery logistics offers a promising avenue for enhancing delivery efficiency. This advancement has garnered considerable interest in the truck−drone cooperative delivery problem. In response, this study delves into the multi-visit vehicle routing problem with multiple heterogeneous drones (MV-VRP-MHD), focused on addressing its feasibility and scalability in real-world, large-scale settings. By considering essential factors such as drones’ ability for multiple deliveries, varied energy consumption patterns, and the employment of heterogeneous drone fleets, our model aims to minimize the overall completion time. To address the challenge of tackling large-scale instances, we introduce a hybrid algorithm that combines variable neighborhood search and simulated annealing (VNS-SA). This algorithm applies a two-phased approach to construct an initial solution and further refines it through the implementation of four unique neighborhood operators. Finally, to confirm the effectiveness of MV-VRP-MHD and VNS-SA, a comprehensive series of computational experiments was carried out. The experiments demonstrated that MV-VRP-MHD significantly enhances the efficiency of last-mile delivery. The analysis results indicate that the heterogeneous drone fleet effectively handles large-area deliveries. It also found that while improvements in drone speed, payload capacity, and battery life were beneficial, incremental enhancements in these areas yielded limited effects when applied individually. Operator experiments revealed that the drone route generation operator was the most effective among the four neighborhood operators. Finally, we discuss the impact of uncertainties in the delivery process on the model results.