Pre-tactical optimization of runway utilization under uncertainty

Efficient planning of runway utilization is one of the main challenges in Air Traffic Management (ATM). It is important because runway is the combining element between airside and groundside. Furthermore, it is a bottleneck in many cases. In this paper, we develop a specific optimization approach for the pre-tactical planning phase that reduces complexity by omitting unnecessary information. Instead of determining arrival/departure times to the minute in this phase yet, we assign several aircraft to the same time window of a given size. The exact orders within those time windows can be decided later in tactical planning. Mathematically, we solve a generalized assignment problem on a bipartite graph. To know how many aircraft can be assigned to one time window, we consider separation requirements for consecutive aircraft types. In reality, however, uncertainty and inaccuracy almost always lead to deviations from the actual plan or schedule. Thus, we present approaches to incorporate uncertainty directly in our model in order to achieve a stabilization with respect to changes in the data. Namely, we use techniques from robust optimization and stochastic optimization. Further, we analyze real-world data from a large German airport to obtain realistic delay distributions, which turn out to be two-parametric Γ-distributions. Finally, we describe a simulation environment to test our new solution methods.