A Study on the Traveling Salesman Problem with a Drone

A promising new model for future logistics networks involves the collaboration between traditional trucks and modern drones. The drone can pick up packages from the truck and deliver them by air while the truck is serving other customers. The operational challenge combines the allocation of delivery locations to either the truck or the drone, and the coordinated routing of the truck and the drone. In this work, we consider the scenario of a single truck and one drone, with the objective to minimize the completion time (or makespan). As our first contribution, we prove that this problem is strongly NP-hard, even in the restricted case when drone deliveries need to be optimally integrated in a given truck route. We then present a constraint programming formulation that compactly represents the operational constraints between the truck and the drone. Our computational experiments show that solving the CP model to optimality is significantly faster than the state-of-the-art exact algorithm. For larger instances, our CP-based heuristic algorithm is competitive with a state-of-the-art heuristic method.