Airports are one of the segments within air transport and their serviceability ensures air transport efficiency. However, airports are among the largest contributors to the negative environmental impact of this kind of transport. Individual activities at airports leave a negative environmental footprint. By optimizing processes, it is possible to reduce the negative environmental impacts of these subjects. Airport winter maintenance is one of the important activities accompanying airports in geographical areas where winter season is expected due to the climate zone and weather conditions. Effective winter maintenance ensures optimal airport operation and has a significant impact on safety. However, the winter maintenance of the airport causes an excessive burden on the environment around the airports, in particular by applying de-icing agents to aircraft and movement areas, or by emissions and noise caused by equipment for snow and ice removal. The aim of the present article is to optimize the winter maintenance of the airport, namely the deployment of winter maintenance equipment with respect to meteorological conditions while maintaining the priorities for winter maintenance between individual airport areas. The aim of optimization is to achieve the saving of maintenance time and reduce the negative environmental impact of winter maintenance by effectively deploying equipment and devices.

We consider inhomogeneous matrix products over max-plus algebra, where the matrices in the product satisfy certain assumptions under which the matrix products of sufficient length be rank-one, as it was shown in [6][L. Shue, B.D.O. Anderson, S. Dey: On steady state properties of certain max-plus products. Proceedings of the American Control Conference, Philadelphia, Pensylvania, (June 1998), 1909 1913.]. We establish a bound on the transient after which this starts to happen for any product of matrices whose length exceeds that bound.