Purpose. The study aims to establish a rational variant for running of specialized train traffic volumes by managing risks and determining the dependence of the train motion interval on locomotive fleet and locomotive crews. It is possible to achieve this purpose by establishing the sequence of stages of the genetic algorithm for implementing a mathematical model for determining the movement intensity of specialized train traffic volumes. Methodology. The study examined the process of passing specialized train traffic volumes along railway corridors as part of a single logistics chain. We approached this process from the perspective of risk management when it is necessary to determine the train arrival time from different directions with the existing technological restrictions. The choice of rational interval between the trains running along the railway corridors is extremely important, since it allows the passage of specialized freight traffic volumes more efficiently in terms of delivery costs to the destination and the speed of this delivery. In order to implement an optimization mathematical model for determining the motion intensity of specialized train traffic volumes in railway directions, a real-coded genetic algorithm (RGA) was used. Findings. The analysis proved the search efficiency of the rational option for establishing the motion intensity of specialized train traffic volumes, taking into account the railway costs for traction and the costs of consignees. A graph of the best and mean values of fitness function on the number of RGA iterations in the process of finding a solution is presented. Originality. As a result of the study, a software implementation of the mathematical model for determining the intensity of specialized train traffic volumes in the railway directions was developed taking into account the balance of rail costs for traction resources and the costs of consignee. This program allows you to simulate the choice of time of trains’ arrival to the final station of from different directions in the uncertainty conditions. An expert analysis of the obtained simulation results proved the adequacy of the solution. Practical value. This study allows us to establish the dependence of train motion interval on the locomotive fleet and locomotive crews. The search for the optimal interval of train traffic volumes using the developed mathematical model makes it possible to manage the associated risks and minimize operating costs on the specialized train traffic volumes.