STUDY OF THE DYNAMICS OF EXPORT METAL PRODUCTS FREIGHT FLOWS AND THEIR MATHEMATICAL MODELING UNDER CONDITIONS OF AN UNSTABLE ENVIRONMENT

Abstract

The article examines how export transportation of metal products by rail changed under conditions of abrupt transformations in the external environment. Particular attention is paid to the state of the transportation process before the onset of large-scale disruptive events and to the way it evolved under their influence, reflecting its gradual adaptation to new operating conditions.

For quantitative assessment, the following statistical indicators were selected: mean value, standard deviation, and coefficient of variation. This approach made it possible not only to determine the transportation volume levels but also to identify the internal irregularity of transportation over time, particularly the periods when fluctuations became sharper and less predictable.

The results indicate that the transportation process underwent significant changes during the study period. Initially, it functioned relatively steadily; however, it later shifted into a phase of pronounced instability. Subsequently, signs of a new operating regime gradually emerged, better adapted to existing conditions. At the same time, the variability of indicators increased, and the nature of their fluctuations changed. Changes in the intra-annual distribution of transportation volumes were also observed, further confirming the non-stationary nature of the process.

To describe these changes, a mathematical model combining a trend component and fluctuations with variable parameters is proposed. This approach makes it possible to simultaneously account for the general development trend and short-term deviations. Model validation demonstrated that it reproduces real dynamics with sufficient accuracy (mean relative error 11,81%, ), indicating its applicability as a practical analytical tool.

Overall, the obtained results contribute to a better understanding of transportation behavior under unstable conditions and may be useful for forecasting and decision-making in logistics management, particularly in situations characterized by uncertainty and variability.