# Integration methods for aircraft scheduling and trajectory optimization at a busy terminal manoeuvring area

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## Abstract

This paper deals with the problem of efficiently scheduling take-off and landing operations at a busy terminal manoeuvring area (TMA). This problem is particularly challenging, since the TMAs are becoming saturated due to the continuous growth of traffic demand and the limited available infrastructure capacity. The mathematical formulation of the problem requires taking into account several features simultaneously: the trajectory of each aircraft should be accurately predicted in each TMA resource, the safety rules between consecutive aircraft need to be modelled with high precision, the aircraft timing and ordering decisions have to be taken in a short time by optimizing performance indicators of practical interest, including the minimization of aircraft delays, travel times and fuel consumption. This work presents alternative approaches to integrate various modelling features and to optimize various performance indicators. The approaches are based on the resolution of mixed-integer linear programs via dedicated solvers. Computational experiments are performed on real-world data from Milano Malpensa in case of multiple delayed aircraft. The results obtained for the proposed approaches show different trade-off solutions when prioritizing different indicators.

## Keywords

Air traffic Take-off and landing operations Optimal control Job shop scheduling Mixed-integer linear programming Pareto efficiency## Notes

### Acknowledgements

The corresponding author thanks the support of the German academic exchange service (DAAD): Research Grant for PhD candidates, Funding Program Number 57130097. The authors also thank the editors and the reviewers of this paper for their remarks, comments and suggestions on how to improve the paper quality. The authors can share the proposed MILP instances with any researcher interested in the studied topic.

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