The study investigated the process of rolling stock movement along a direction and took into consideration possible risks during transportation of freight. It revealed the main reasons, which cause effects of the first and last mile. They include, namely, the lack of the required number of technically sound rolling stock on scheduled time and significant difficulties with the passage of trains, specifically through port and border stations. The study formalized the technological process of transportation of freight along a direction in the form of an optimization mathematical model of the process of movement of freight wagons. The objective function of the model represented total operation costs. Its basis was the Lebesgue-Stieltjes integral, which took into consideration the effect of the first and last mile. The model also took into consideration possible risks, which arise in the process of wagon operation. It is expedient to refer the built optimization model to the problems of stochastic programming. The analysis of statistical data showed that the time required for wagons to move from an initial station of a route to a port station and the time required for movement of wagons from a port station directly to a port conform to normal distribution. The presence of a positive correlation between these two values gave reason to consider the corresponding parameters within a single probabilistic field. This approach made possible to determine probability of untimely arrival of wagons to a port more accurately and, accordingly, to determine a value of financial risk. The modeling proved that there was an extremum of the objective function of the minimum type, which made possible to form a procedure for optimal control of transport parameters. Thus, the generated model is universal in nature. It gives possibility to manage the transportation process with the lowest operational costs for the railway in the presence of feedback. Calculations showed a decrease in railway costs approximately by 10 % comparing with the costs calculated according to the existing method of determination of the actual cost of transportation of freight. The optimization model is the basis for formation of an automated technology for the management of freight traffic. We propose to implement it in the form of a system of decision support for the dispatcher staff