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.
The work of @cite_13 is concerned with creating drone delivery models for health-care to locate a warehouse with supplies and drone nests to complete final delivery. They developed two models to the problem; the first one has an objective to minimize the total weighted delivery time, i.e., road covered by the truck plus air covered by the drone. The second model intends to minimize the maximum weighted time for truck drone delivery subject to a budget and drone travel distance constraint.
@cite_13
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The use of unmanned aerial vehicles (UAVs) as delivery systems of online goods is rapidly becoming a global norm, as corroborated by Amazon's “Prime Air” and Google's “Project Wing” projects. However, the real-world deployment of such drone delivery systems faces many cyber-physical security challenges. In this paper, a novel mathematical framework for analyzing and enhancing the security of drone delivery systems is introduced. In this regard, a zero-sum network interdiction game is formulated between a vendor, operating a drone delivery system, and a malicious attacker. In this game, the vendor seeks to find the optimal path that its UAV should follow, to deliver a purchase from the vendor's warehouse to a customer location, to minimize the delivery time. Meanwhile, an attacker seeks to choose an optimal location to interdict the potential paths of the UAVs, so as to inflict cyber or physical damage to it, thus, maximizing its delivery time. First, the Nash equilibrium point of this game is characterized. Then, to capture the subjective behavior of both the vendor and attacker, new notions from prospect theory are incorporated into the game. These notions allow capturing the vendor's and attacker's i) subjective perception of attack success probabilities, and ii) their disparate subjective valuations of the achieved delivery times relative to a certain target delivery time. Simulation results have shown that the subjective decision making of the vendor and attacker leads to adopting risky path selection strategies which inflict delays to the delivery, thus, yielding unexpected delivery times which surpass the target delivery time set by the vendor. We address the problem of managing a drone-based delivery process. We consider the specific situation of a delivery company, that uses a set of trucks equipped with a given number of drones. In particular, items of a limited weight and size could be delivered by using drones. A vehicle, during its trip, can launch a drone when serving a customer, the drone performs a delivery for exactly one customer and returns to the vehicle, possibly at a different customer location. Each drone can be launched several times during the vehicle’s route. It is imposed a limit on the maximum distance that each drone can travel and synchronization requirements between vehicle and drone should be ensured. In particular, it is assumed that a vehicle waits for a drone for a maximum period of time. The aim is to serve all customers within their time window. The problem is modeled as a variant of the vehicle routing problem with time windows. The aim of this work is to analyze the delivery process with drones, by taking into account the total transportation cost and highlighting strategical issues, related to the use of drones. The numerical results, collected on instances generated to be very close to reality, show that the use of drones is not economically convenient in the classical terms. However, when considering negative externalities related to the use of classical vehicles and quality of service requirements, the benefit of using drones becomes relevant. 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. 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.