Hexaly on the Aircraft Landing Problem

Benchmarks Airline Scheduling

Chloé Optimization Scientist July 21, 2026

Hexaly is the solver of choice to tackle large-scale scheduling problems. As an example, we show here the efficiency of Hexaly on the Aircraft Landing Problem. This problem is described in the “Scheduling aircraft landings – the static case” article by J. E. Beasley, M. Krishnamoorthy, Y. M. Sharaiha, and D. Abramson (2000), Transportation Science 34(2), pp. 180-197. The test instances come from the OR-Library maintained by J. E. Beasley.

In the Aircraft Landing Problem, landing times for a set of planes must be scheduled. Each plane can land within a predetermined time window around a target time, and a separation time must be observed between successive planes. There are earliness and tardiness costs to pay for each plane landing before or after its target time. The objective is to minimize the total penalty cost.

On the Aircraft Landing Problem, Hexaly achieves an average gap of 1.1% to the best known solutions in the research community (BKS) in 1 minute of runtime.

The given problem instances, ranging from 10 to 500 planes to schedule, have been tested with Hexaly 14.5 on a server equipped with an AMD Ryzen 7 7700 processor (8 cores, 3.8 GHz, 8 MB cache) and 32 GB of RAM.

Hexaly results on the Aircraft Landing Problem

For instances 1-8, Hexaly finds BKS within a few seconds of runtime. For larger instances ranging from 100 to 500 planes, the gap to BKS, expressed as a percentage, across different time limits, is shown in the figure below. Note that BKS are computed using dedicated algorithms, with arbitrary long running times and on specific hardware.

This last figure presents the solution obtained on instance 9 with 100 planes.

You can find the complete model of the Aircraft Landing Problem in Python, Java, C#, C++, and HXM in our Example Tour.