Drones have been used in new types of transportation services such as drone-based package delivery and air transportation. One of the necessary elements for the drone-based transportation service system is a vertiport, which is a designated area for take-off and landing of drones. In the early phase of planning a network of vertiports, it is important to consider midair congestion of drone traffic in order to avoid the risk of collisions, because the risk increases complexity in scheduling and routing in the subsequent operations phase.
In this study, we propose a novel hub location problem that incorporates congestion occuring by interactions between hub-to-hub arcs. Our original formulation contains nonconvex bilinear terms, which is hard to solve. However, by exploiting the property of an optimal solution, we linearize the original problem using Reformulation-Linearization Technique. Even though we obtain a linearized version of the original problem, the problem still quickly becomes intractable as the size of the problem increases. To overcome the large-size problem, we develop a heuristic algorithm based on a genetic algorithm. Using numerical examples, we demonstrate that considering collision risks has a significant impact on the quality of the location solution derived from the mathematical model and confirm the improved performance of the heuristic algorithm.