Coordinated logistics with a truck and a drone

We determine the efficiency of a delivery system in which an unmanned aerial vehicle (UAV), or a fleet of UAVs, provides service to customers while making return trips to a truck that is itself moving. In other words, a UAV picks up a package from the truck (which continues on its route), and after delivering the package, the UAV returns to the truck to pick up the next package. Although the hardware for such systems already exists, it is not yet understood to what extent such an approach can actually provide a significantly improved quality of service. By combining a theoretical analysis in the Euclidean plane with real-time numerical simulations on a road network, we conclude that the improvement in efficiency due to introducing a UAV is proportional to the square root of the ratio of the speeds of the truck and the UAV.