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.
Drone routing papers, such as @cite_32 and @cite_7 , typically focus on surveillance applications. The FSTSP @cite_3 considers a delivery scenario based on combining drone delivery with a delivery truck. There do not appear to be papers that focus solely on using drones to make deliveries. This existing work on drone routing ignores factors important to drone delivery such as vehicle capacity, battery weight, changing payload weight, and reusing vehicles to reduce costs.
@cite_3 @cite_32 @cite_7
1977319619 2964117926 2053083032
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. We consider a single Unmanned Aerial Vehicle (UAV) routing problem where there are multiple depots and the vehicle is allowed to refuel at any depot. The objective of the problem is to find a path for the UAV such that each target is visited at least once by the vehicle, the fuel constraint is never violated along the path for the UAV, and the total fuel required by the UAV is a minimum. We develop an approximation algorithm for the problem, and propose fast construction and improvement heuristics to solve the same. Computational results show that solutions whose costs are on an average within 1.4 of the optimum can be obtained relatively fast for the problem involving five depots and 25 targets. Aerial robotics can be very useful to perform complex tasks in a distributed and cooperative fashion, such as localization of targets and search of point of interests (PoIs). In this work, we propose a distributed system of autonomous Unmanned Aerial Vehicles (UAVs), able to self-coordinate and cooperate in order to ensure both spatial and temporal coverage of specific time and spatial varying PoIs. In particular, we consider an UAVs system able to solve distributed dynamic scheduling problems, since each device is required to move towards a certain position in a certain time. We give a mathematical formulation of the problem as a multi-criteria optimization model, in which the total distances traveled by the UAVs (to be minimized), the customer satisfaction (to be maximized) and the number of used UAVs (to be minimized) are considered simultaneously. A dynamic variant of the basic optimization model, defined by considering the rolling horizon concept, is shown. We introduce a case study as an application scenario, where sport actions of a football match are filmed through a distributed UAVs system. The customer satisfaction and the traveled distance are used as performance parameters to evaluate the proposed approaches on the considered scenario.