Hexaly on the Aircraft Landing Problem

Benchmarks Airline Scheduling

Chloé Optimization Scientist April 9, 2026

Hexaly is the solver of choice to tackle large-scale scheduling problems. As an example, we show here the efficiency of Hexaly Optimizer 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, the landing times of a set of planes have to 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 reaches a 1.1% average gap to the optimal solutions in 1 minute of running time with instances up to 500 planes.

The given problem instances, counting 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, 3.8GHz, 8MB cache) and 32GB RAM.

Hexaly results on the Aircraft Landing Problem

For instances 1 to 8, Hexaly finds the optimal solution within a few seconds. For larger instances, ranging from 100 to 500 planes, the gap to the best known solution, expressed in %, for different time limits is shown in the figure below. Note that the state-of-the-art solutions 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.