Technological advances for unmanned aerial vehicles, commonly referred to as drones, have opened the door to a number of new and interesting applications in areas including military, healthcare, communications, cinematography, emergency response, and logistics. However, limitations due to battery capacity, maximum take-off weight, finite range of wireless communications, and legal regulations have restricted the effective operational range of drones in many practical applications.

Several hybrid operational models involving one or more drones launching from a larger vehicle, which may be a ship, truck, or airplane, have emerged to help mitigate these range limitations. In particular, the drones utilize the larger vehicle as both a mobile depot and a recharging or refueling platform. In this dissertation, we describe routing models that leverage the tandem of one or more drones with a larger vehicle. In these models, there is generally a set of targets that should be visited in an efficient (usually time-minimizing) manner. By using multiple vehicles, these targets may be visited in parallel thereby reducing the total time to visit all targets.

The vehicle routing problem with drones (VRPD) and traveling salesman problem with a drone (TSP-D) consider hybrid truck-and-drone models of delivery, where the goal is to minimize the time required to deliver a set of packages to their respective customers and return the truck(s) and drone(s) to the origin depot. In both problems, the drone can carry one homogeneous package at a time. Theoretical analysis, exact solution methods, heuristic solution methods, and computational results are presented. In the mothership and drone routing problem (MDRP), we consider the case where the larger launch vehicle is free to move in Euclidean space (the open seas) and launch a drone to visit one target location at a time, before returning to the ship to pick up new cargo or refuel. The mothership and high capacity drone routing problem (MDRP-HC) is a generalization of the mothership and drone routing problem, which allows the drone to visit multiple targets consecutively before returning to the ship. MDRP and MDRP-HC contain elements of both combinatorial optimization and continuous optimization. In the multi-visit drone routing problem (MVDRP), a drone can visit multiple targets consecutively before returning to the truck, subject to energy constraints that take into account the weight of packages carried by the drone.