Abstract
The paper considers the problem of optimal redistribution of transit container flows on the railway network. The problem is proposed to be solved as the problem of a multi-commodity flow of minimum cost using the relaxation method. The relaxation method allows choosing the most efficient variant of the next solution at each iteration step. To search for the optimal distribution of container flows on the network, graph theory was used, i.e., the network is presented as a multigraph with a set of vertices and arcs, for which the costs of transporting a unit of production, the maximum and minimum values of the flows between the vertices are given, the conditions for maintaining the flow at the vertices of the graph and restrictions on the amount of flow along the arcs are given. It has been established that in order to implement the task, it is necessary to take into account the unit costs for the movement of container flows between the nodes of the railway network, taking into account the capacity of the branches between the junction stations. The developed mathematical model for the redistribution of container traffic allows you to identify areas with limited throughput, develop options for optimization measures, and, as a result, achieve an economic effect by reducing the cost of transporting containerized cargo.