Disjunctive linear separation conditions and mixed-integer formulations for aircraft conflict resolution

•Formalize disjunctive linear separation conditions for aircraft conflict resolution.•Characterize pairwise aircraft conflict-free trajectories based on velocity bounds.•Propose exact solution methods for the 2D aircraft conflict resolution problem.•Lexicographic optimization approach for extended problem with flight level changes.•Show that the proposed methods outperform state-of-the-art approaches.