The vehicle routing problem with drones: Extended models and connections

Abstract

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

Optimization approaches for civil applications of unmanned aerial vehicles (UAVs) or aerial drones: A survey

“…The derived bounds are similar to Amdahl's law on the maximum speed‐up potential for computer programs via parallelization . Poikonen et al also examine maximum potential savings in the case of different distance metrics for trucks and drones, in the case of a limited battery life, and for a general objective function that considers not only the makespan, but also variable costs of truck and drone deployment per unit of time. The authors also establish connections between the VRP with a drone and the well‐studied min–max vehicle routing and the min–max close‐enough VRPs.…”

“…Wang et al and Poikonen et al extended the problem setting to the VRP with a drone. They perform worst‐case analyses; for example, they estimate the best possible reduction in delivery completion time if truck operations are combined with drone operations compared to truck operations only.…”

A variable neighborhood search for flying sidekick traveling salesman problem

“…Poikonen et al. () extend the description of the theorems comparing different drone configurations in the delivery process to determine the maximum benefit. For example, they study the trade‐off between speed and the number of drones, that is, they compare what is better, a more significant number of slower drones or a smaller number of faster drones.…”

Drone delivery from trucks: Drone scheduling for given truck routes

“…They provide a novel MIP model and some further heuristics, for which worst‐case approximation guarantees are found. Worst‐case results are also presented by Wang et al and Poikonen et al . They, however, treat the multitruck case where each truck may also host more than a single drone.…”