The orienteering problem with drones

We extend the classical problem setting of the orienteering problem (OP) to incorporate multiple drones that cooperate with a truck to visit a subset of the input nodes. We call this problem the OP with multiple drones (OP-mD). Drones have a limited battery endurance, and thus, they can either move together with the truck at no energy cost for the battery or be launched by the truck onto short flights that must start and end at different customer locations. A drone serves exactly one customer per flight. Moreover, the truck and the drones must wait for each other at the landing locations. A customer prize can be collected at most once, either upon visiting it by the truck or upon serving it by a drone. Similarly to the OP, we maximize the total collected prize under the condition that the truck and the drones return to the depot within a given amount of time. We provide a mixed-integer linear programming formulation for the OP-mD and devise a tailored branch-and-cut algorithm based on a novel decomposition of the problem. We solve instances of the OP-mD with up to 50 nodes within one hour of CPU time with a standard computational setup. Finally, we adapt our framework to solve closely related problems in the literature and compare the resulting computational performance with that of previous studies.