Heuristics for flights arrival scheduling at airports

We develop an efficient matheuristic algorithm for the aircraft landing problem (ALP). The ALP aims to schedule aircraft landings such that the total deviation from target arrival times is minimized. We propose a relax-and-solve (R&S) algorithm that operates by performing a set of "relax" and "solve" iterations. The relax procedure destructs a sequence of aircraft landings, and the solve procedure re-constructs a complete sequence and schedules the aircraft landings. We compare the proposed algorithm and the state-of-the-art algorithm for the ALP and also the solver CPLEX, and show that our algorithm obtains all best-known solutions within one minute, even for instances including 500 aircraft. Those characteristics of the algorithm are very important for practical settings. In particular, the typical short time window available for planning the aircraft landings at busy airports demands quick delivery of quality landing schedules (or updating the current schedule), and fast and effective algorithms are therefore paramount.