Optimal sequencing of aircrafts take-off and landing at a busy airport

This paper studies the problem of sequencing aircraft take-off and landing operations at congested airports. We introduce and analyze alternative detailed formulations and solution algorithms for scheduling arrival and departure times of the aircrafts, such that the delay with respect to the scheduled times is minimized. The aircraft scheduling problem (ASP) is viewed as an extension of the job shop scheduling problem with additional real-world constraints and formulated by using alternative graphs. Two alternative formulations model the required time separation among aircrafts in air segments and runways according to safety regulations and differ for the level of detail used to represent the holding circles. Scheduling rules, heuristic and exact methods are implemented and tested on practical size instances of the Fiumicino airport, the busiest airport in Italy. We show that two versions of an innovative branch and bound algorithm are always able to find good solutions in a few seconds and often improve the best solution computed by the scheduling heuristics. Optimality is proved in less than two minutes for more than half of the instances.