A novel mixed-integer programming approach for the aircraft landing problem

Abstract

Due to the upward trend in the aviation industry, the existing approaches for air traffic control need to be improved to achieve efficient schedules. This paper deals with the aircraft landing problem, which consists of determining a landing time for each aircraft within the radar range of an airport and allocating it to a runway. We propose an exact solution approach that involves mixed-integer linear programming. The objective is hereby to minimize the sum of weighted deviations from the target landing times under consideration of different safety, efficiency and fairness constraints. Despite of the problem’s NP-hardness, our method exhibits low execution times thanks to a modified modeling strategy and provides near-optimal results. Numerical experiments prove efficiency of the approach for different large airports.

Piecewise linear value function approximations in nonlinear dynamic scheduling problems with VTOLs

“…The authors of [3] and [4] deal, for instance, with optimal trajectory planning for aircraft using the Hamilton-Jacobi-Bellman (HJB) equation. [5] and [6] in turn present exact methods for coordination of multiple landing aircraft. However, the class of coupled scheduling and optimal control problems has not been extensively researched in the literature to the best of the authors' knowledge.…”