Scheduling problems of aircraft on a same runway and dual runways

In this paper, the scheduling problems of landing and takeoff aircraft on a same runway and on dual runways are addressed. In contrast to the approaches based on mixed-integer optimization models in existing works, our approach focuses on the minimum separation times between aircraft by introducing some necessary assumptions and new concepts including relevance, breakpoint aircraft, path and class-monotonically-decreasing sequence. Four scheduling problems are discussed including landing scheduling problem, takeoff scheduling problem, and mixed landing and takeoff scheduling problems on a same runway and on dual runways with the consideration of conversions between different aircraft sequences in typical scenarios. Two real-time optimal algorithms are proposed for the four scheduling problems by fully exploiting the combinations of different classes of aircraft, and necessary definitions, lemmas and theorems are presented for the optimal convergence of the algorithms. Numerical examples are presented to show the effectiveness of the proposed algorithms. In particular, when 100 aircraft are considered, by using the algorithm in this paper, the optimal solution can be obtained in less than 5 seconds, while by using the CPLEX software to solve the mix-integer optimization model, the optimal solution cannot be obtained within 1 hour.