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The vehicle routing problem with drones (VRPD) is inspired by the increasing interest in commercial drone delivery by companies such as Amazon, Google, DHL, and Walmart. In our model, a fleet of m homogeneous trucks each carries k drones with a speed of α times that of the truck. Each drone may dispatch from the top of the truck and carry a package to a customer location. The drone then returns to the top of its truck to recharge or swap batteries (we assume instantaneously). The truck itself is allowed to move and deliver packages, but must be stationary at a delivery location or the depot when launching or retrieving drones. The goal is to minimize the completion time to deliver all packages and return all vehicles back to the central depot. In this article, we review and extend several worst‐case results from an earlier paper and we make connections with another practical variant of the vehicle routing problem and with Amdahl's Law. We find that the VRPD model offers some important practical advantages. The drones allow the truck to parallelize tasks and they are able to take advantage of crow‐fly distances. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(1), 34–43 2017

The Traveling Salesman Problem with a Drone (TSP-D) is a hybrid truck and drone model of delivery, in which the drone rides on the truck and launches from the truck to deliver packages. Our approach to the TSP-D uses branch and bound, whereby each node of the branch-and-bound tree corresponds with a potential order to deliver a subset of packages. An approximate lower bound at each node is given by solving a dynamic program. We provide additional variants of our heuristic approach and compare solution quality and computation times. Consideration is given to various input parameters and distance metrics. The online supplement is available at https://doi.org/10.1287/ijoc.2018.0826 .

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