Locating Drone Stations for a Truck-Drone Delivery System in Continuous Space

Truck-drone delivery systems have been proposed for sustainable and economical last-mile distribution, especially in urban environments. To widen the service range, some works have recommended adding facilities, such as drone stations, considering the problem in discrete space by choosing from a predefined set. In this article, an evolutionary optimization approach to the design decision of where to locate drone stations in the continuous plane is introduced, modeled, and solved. Drone stations serve as facilities for storage, charging, and launching. A truck (or other land transport means) transports parcels to the drone stations from a depot and the drones launch from the stations and deliver the parcels to each customer. The objective is to determine the positions of the drone stations in 2-D space and establish the shortest fixed truck route from the depot through all the stations and returning to the depot. The problem is constrained by the radius of service for each drone and all customers must be served, if possible. We formulate the problem as a constrained nonlinear optimization problem and present two versions of an algorithm using particle swarm optimization (PSO) with a subordinate dynamic program. Computational results show that our approach achieves much better results than a standard commercial nonlinear solver in a similar amount of computational time for both maximizing coverage of customers and minimizing distance of the truck delivery route. A design case study concerning healthcare delivery throughout the Birmingham, Alabama (USA) metropolitan area is provided.