Trucks and drones cooperation in the last-mile delivery process

We address the problem of routing a fleet of trucks equipped with unmanned aerial vehicles, commonly known as drones, to perform deliveries in last-mile delivery process. The customers can be served by either a truck or a drone within the respective time window of each. Each capacitated truck carries drones that can be launched to perform deliveries. The drone takes off from a truck located either at a customer or at the depot and it must land on the same truck after visiting a customer to be served. The aim is to serve all customers at minimum cost, under time window, capacity, and flying endurance constraints. We formulate the problem as a mixed integer linear program (MILP) and develop a heuristic procedure where a two-phase strategy is embedded in a multi-start framework. The computational results are carried out on instances generated by starting from vehicle routing problem with time windows benchmarks. We analyze the behavior of the considered transportation system by mean of the solutions provided by the MILP. The proposed formulation is able to solve instances with up to 15 customers. The solutions of the MILP are used as benchmark to assess the effectiveness of the proposed heuristic procedure.