Summary: On-demand air mobility services, often called air taxis, are on the way to revolutionize our urban/regional transportation sector by lifting transportation to the third dimension and thus possibly contribute to solving the congestion-induced transportation deadlock many metropolitan regions face today. Although existing research mainly focuses on the design of efficient vehicles and specifically battery technology, in the near future, a new question will arise: Where to locate the vertiports/landing pads for such air taxis? In this study, we propose a vertiport location selection problem. In contrast to existing studies, we allow the demand to be distributed over the whole metropolitan area, modeled as a grid, and exclude certain grid cells from becoming hubs, for example, because of safety/geographical constraints. The combination of these two contributions makes the problem intriguingly difficult to solve with standard solution techniques. We propose a novel variable neighborhood search heuristic, which is able to solve \(12 \times 12\) grid instances within a few seconds of computation time and zero gaps in our experiments, whereas CPLEX needs up to 10 hours. We believe that our study contributes toward the scalable selection of vertiport locations for air taxis.
Summary of contribution: The increasing interest in opening the third dimension, that is, altitude, to transportation inside metropolitan regions raises new research challenges. Existing research mainly focuses on the design of efficient vehicles and control problems. In the near future, however, the actual operation of air taxis will lead to new set of operations research problems for so-called air taxi operations. Our contribution focuses on the optimization of vertiports for air taxi operations in a metropolitan region. We choose to model the problem over a grid-like demand structure, with a novel side constraint: selected grid cells are unavailable as hubs, for example, because of environmental, technical, cultural, or other reasons. This makes our model a special case in between the two traditional models: discrete location and continuous location. Our model is inherently difficult to solve for exact methods; for instance, solving a grid of \(12 \times 12\) grid cells needs more than 10 hours with CPLEX, when modeled as a discrete location problem. We show that a straightforward application of existing neighborhood search heuristics is not suitable to solve this problem well. Therefore, we design an own variant of mixed variable neighborhood search, which consists of novel local search steps, tailored toward our grid structure. Our evaluation shows that by using our novel heuristic, almost all instances can be solved toward optimality.