Vehicle routing problem with drones

The vehicle routing problem with drones (VRPD) is an extension of the classic capacitated vehicle routing problem, where not only trucks but drones are used to deliver parcels to customers. One distinctive feature of the VRPD is that a drone may travel with a truck, take off from its stop to serve customers, and land at a service hub to travel with another truck as long as the flying range and loading capacity limitations are satisfied. Routing trucks and drones in an integrated manner makes the problem much more challenging and different from classical vehicle routing literature. We propose a mixed integer programming model, and develop a branch-and-price algorithm. Extensive experiments are conducted on the instances randomly generated in a practical setting, and the results demonstrate the good computational performance of the proposed algorithm. We also conduct sensitivity analysis on a key factor that may affect the total cost of a solution.