Nested Vehicle Routing Problem: Optimizing Drone-Truck Surveillance Operations

Unmanned aerial vehicles or drones are becoming increasingly popular due to their low cost and high mobility. In this paper we address the routing and coordination of a drone-truck pairing where the drone travels to multiple locations to perform specified observation tasks and rendezvous periodically with the truck to swap its batteries. We refer to this as the Nested-Vehicle Routing Problem (Nested-VRP) and develop a Mixed Integer Programming (MIP) formulation with critical operational constraints, including drone battery capacity and synchronization of both vehicles during scheduled rendezvous. Given the NP-hard nature of the Nested-VRP, we propose an efficient neighborhood search (NS) heuristic where we generate and improve on a good initial solution (i.e., where the optimality gap is on average less than 6% in large instances) by iteratively solving the Nested-VRP on a local scale. We provide comparisons of both the MIP and NS heuristic methods with a relaxation lower bound in the cases of small and large problem sizes, and present the results of a computational study to show the effectiveness of theMIPmodel and the efficiency of the NS heuristic, including for a real-life instance with 631 locations. We envision that this framework will facilitate the planning and operations of combined drone-truck missions.