The efficiency and dynamism of Unmanned Aerial Vehicles (UAVs), or drones, present substantial application opportunities in several industries in the last years. Notably, the logistic companies gave close attention to these vehicles envisioning reduce delivery time and operational cost. A variant of the Traveling Salesman Problem (TSP) called Flying Sidekick Traveling Salesman Problem (FSTSP) was introduced involving drone-assisted parcel delivery. The drone is launched from the truck, proceeds to deliver parcels to a customer and then is recovered by the truck in a third location. While the drone travels through a trip, the truck delivers parcels to other customers as long as the drone has enough battery to hover waiting for the truck. This work proposes a hybrid heuristic that the initial solution is created from the optimal TSP solution reached by a TSP solver. Next, an implementation of the General Variable Neighborhood Search is used to obtain the delivery routes of truck and drone. Computational experiments show the potential of the algorithm to improve the delivery time significantly. Furthermore, we provide a new set of instances based on well-known TSPLIB instances.
Another variant for the problem is the Drone Delivery Problem (DDP) by @cite_16 where only drones perform the delivery. The distribution center is the return point of routes, where the delivery man changes the battery of the UAV and loads it with another parcel. Moreover, drones can visit a location only once, and perform multiple trips per route. The paper provides a MILP implementation for small instances and for large ones a SA heuristic was proposed to find suboptimal solutions to the DDP within a limited run time.
@cite_16
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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 Unmanned aerial vehicles, or drones, have the potential to significantly reduce the cost and time of making last-mile deliveries and responding to emergencies. Despite this potential, little work has gone into developing vehicle routing problems (VRPs) specifically for drone delivery scenarios. Existing VRPs are insufficient for planning drone deliveries: either multiple trips to the depot are not permitted, leading to solutions with excess drones, or the effect of battery and payload weight on energy consumption is not considered, leading to costly or infeasible routes. We propose two multitrip VRPs for drone delivery that address both issues. One minimizes costs subject to a delivery time limit, while the other minimizes the overall delivery time subject to a budget constraint. We mathematically derive and experimentally validate an energy consumption model for multirotor drones, demonstrating that energy consumption varies approximately linearly with payload and battery weight. We use this approximation to derive mixed integer linear programs for our VRPs. We propose a cost function that considers our energy consumption model and drone reuse, and apply it in a simulated annealing (SA) heuristic for finding suboptimal solutions to practical scenarios. To assist drone delivery practitioners with balancing cost and delivery time, the SA heuristic is used to show that the minimum cost has an inverse exponential relationship with the delivery time limit, and the minimum overall delivery time has an inverse exponential relationship with the budget. Numerical results confirm the importance of reusing drones and optimizing battery size in drone delivery VRPs. Abstract Once limited to the military domain, unmanned aerial vehicles are now poised to gain widespread adoption in the commercial sector. One such application is to deploy these aircraft, also known as drones, for last-mile delivery in logistics operations. While significant research efforts are underway to improve the technology required to enable delivery by drone, less attention has been focused on the operational challenges associated with leveraging this technology. This paper provides two mathematical programming models aimed at optimal routing and scheduling of unmanned aircraft, and delivery trucks, in this new paradigm of parcel delivery. In particular, a unique variant of the classical vehicle routing problem is introduced, motivated by a scenario in which an unmanned aerial vehicle works in collaboration with a traditional delivery truck to distribute parcels. We present mixed integer linear programming formulations for two delivery-by-drone problems, along with two simple, yet effective, heuristic solution approaches to solve problems of practical size. Solutions to these problems will facilitate the adoption of unmanned aircraft for last-mile delivery. Such a delivery system is expected to provide faster receipt of customer orders at less cost to the distributor and with reduced environmental impacts. A numerical analysis demonstrates the effectiveness of the heuristics and investigates the tradeoffs between using drones with faster flight speeds versus longer endurance. In this paper, we introduce the vehicle routing problem with drones (VRPD). A fleet of trucks equipped with drones delivers packages to customers. Drones can be dispatched from and picked up by the trucks at the depot or any of the customer locations. The objective is to minimize the maximum duration of the routes (i.e., the completion time). The VRPD is motivated by a number of highly influential companies such as Amazon, DHL, and Federal Express, actively involved in exploring the potential use of commercial drones for package delivery. After stating our simplifying assumptions, we pose a number of questions in order to study the maximum savings that can be obtained from using drones; we then derive a number of worst-case results. The worst-case results depend on the number of drones per truck and the speed of the drones relative to the speed of the truck.