Vehicle routing with multiple UAVs for the last-mile logistics distribution problem: hybrid distributed optimization

The logistics market stands to benefit from the accessibility and increased use of new technologies. As technology continues to advance, drones have emerged as a notable innovation. Within the logistics field, there is growing interest in leveraging drones, particularly for handling small and medium-sized orders such as mobile phones. The appeal of drones lies in their economic and environmental advantages, attributed to their reduced energy consumption. These unmanned aerial vehicles are considered a valuable component of the ongoing technological revolution in transportation, with the potential to enhance the efficiency of last-mile deliveries. To explore their applicability, mixed vehicle-drone distribution models have surfaced as a promising alternative to traditional delivery methods. These models enable companies to minimize transportation costs by leveraging the strengths of both vehicles and drones. In this study, we present a solution to the vehicle routing model with multiple drones (VRPm-D). Our objective is to efficiently transport a specified quantity of products from a central depot to customers by devising optimal routes for both trucks and drones. The study focuses on employing a VRPm-D model to facilitate the transportation process, involving a predetermined fleet of vehicles and drones. The vehicles start and end their routes at a central depot. The primary goal is to minimize the time taken by trucks utilizing drones to cater to the needs of every customer effectively while considering the payload capacity and energy endurance constraints of the drones. To address these objectives, we propose a hybrid vehicle-drone routing problem formulated using the genetic clustering algorithm (HVDRP-GCA). This approach aims to optimize the routes and schedules for both vehicles and drones, taking into account the aforementioned constraints. Our results demonstrate that the processing time exponentially increases as the number of customers grows, particularly noticeable in routes with five or more customers. Importantly, the HVDRP-GCA model outperforms existing methods in the literature, providing favorable outcomes. The results highlight the dominance of our proposed model compared to previous approaches found in the literature.