Vehicle routing problem with drones considering time windows

The cooperation of trucks and unmanned aerial vehicles (UAV) has become a new delivery method in the area of logistics and transportation. In this form of cooperation, the trucks are not only able to provide services to the customers, but also serve as a `launch pad' for the drones, in which the drones can be launched to service a customer and then recovered at the rendezvous node. This study intends to explore this cooperation by developing a model for the vehicle routing problem with drones that considers the presence of customer time windows (VRPTWD). A mixed-integer programming (MIP) model is presented to minimize the total travelling costs. Then, a simple yet effective variable neighborhood search (VNS) procedure with a novel solution representation is proposed as a solver. The numerical results indicate the ability of the proposed VNS to solve the VRPTWD, as well as the improvement of delivery performance using drones.