A Dantzig-Wolfe Reformulation for Automated Aircraft Arrival Routing and Scheduling

Abstract: We consider the problem of computing aircraft arrival routes in a terminal maneuvering area (TMA) together with an automated scheduling of all the arrivals within a given time interval. The arrival routes are modeled as energy-efficient continuous-descent operations, such that separation based on wake-turbulence categories is guaranteed within the TMA. We propose a new model based on a Dantzig-Wolfe reformulation of a previous model for this problem. As in the previous model, we include tree consistency across consecutive planning intervals. However, the reformulation enables us to further improve the model and also consider aircraft that remain in the TMA from the previous period, a feature critical for operational safety. In computational experiments for Stockholm Arlanda airport, the new model consistently outperforms the previous one: we obtain solutions within 5 seconds to 12.65 minutes compared to 40.9 hours with the old model for instances of half hours with high traffic. In addition, we are able to solve instances of a full hour of arriving aircraft with high traffic (33 aircraft) within 22.22 to 58.57 minutes, whereas the old model could not solve these instances at all. While we schedule all aircraft as continuous-descent arrivals, our model can be applied to any type of speed profiles for the arriving aircraft.