Formation of multi-group trains is aimed at arranging their cars in a given order and is one of the mass operations performed at railway. In this regard, the reduction of the duration of shunting operations for the formation of multi-group trains is an urgent task for railway transport. In this paper, for a discrete deterministic-controlled system that simulates the operation of the flat yard, a mathematical statement of the problem of choosing the optimal order of multigroup train formation is obtained. The set of possible states of the system under study and the transitions between them are presented in the form of directed graph, which made it possible to reduce the problem of choosing the order of train formation to the problem of searching the shortest paths on the graph. An algorithm of searching the optimal order of train formation is proposed.

The peculiarity of the transit freight transportation by rail in international traffic is the fact that while performing transportation, the railway administrations are in competition among themselves. At the same time, the routes of cargo traffic volumes significantly depend on the conditions of transportation by railways of individual states. The mathematical model for the distribution of transit freight traffic volumes on the railway network, based on the methods of graph theory and game theory, was proposed in this article. The developed model enables the evaluation of the possibilities of attracting transit freight traffic volumes by individual railway administrations by changing the tariff value and transportation conditions. 110

Ukraine has undertaken the implementation of European Union Directives, which provide non-discriminatory admission to the railway infrastructure of independent carriers. A significant number of factors considerably affect working conditions of the carriers which are independent of Ukrzaliznytsia. One of the goals while performing transportation by independent carriers is the organization of private locomotives operation and their service by engine crews. The purpose of the article is to assess technical and economic indices of private locomotives use for goods transportation. The schemes of infrastructure objects arrangement for locomotives operation and engine crews work are presented. Performed calculations show the potential possibility of independent railway carriers to fulfil transportation to seaports with the use of its private locomotive infrastructure exclusively. The estimation of economically expedient volumes of cargo transportation by private locomotives in comparison with existing pricing of Ukrzaliznytsia is carried out. The nonlinear dependence of transportation volume depending on the distance is determined, at which the total cost of cargo transportation by Ukrzaliznytsia locomotives is equal to the cost of cargo transportation by private locomotives. The results of the study allow concerned companies to evaluate the investment efficiency into the development of locomotive fleet for rail transportation.

Purpose. To improve the method for calculating the time standard for shunting cars from track to track in order to take into account the local operating conditions of railway stations and railway sidings. Methodology. During the research, the methods of theory of railway operation were used. The problem of calculating the time standard for shunting operation was solved as the problem of searching the optimal division of train set into the car groups to achieve minimal time consumption for shunting operation. Findings. In the course of the study, the methods for calculating the time standards for initial and final operations, as well as movements performed when shunting cars from track to track were improved. It was proved that the minimum time spent on shunting cars from track to track was achieved when the train set was divided into the minimum possible number of parts and the cars were shunted in the longest possible groups and one remaining group. It was also established that with sufficient accuracy for engineering problems the duration of shunting train set from track to track can be represented by the piecewise linear function of the car number in it. Originality. The work originality consists in improving the method for calculating the time standard for shunting cars from track to track, that, unlike the existing one, takes into account the length limitations of the car groups being shunted from track to track, as well as the actual composition of operations performed in the process of shunting. Practical value. The use of the developed method allows setting time standards for shunting cars from track to track, taking into account the local operating conditions of railway stations and sidings of industrial enterprises. The method also makes it possible to simplify solving problems of searching the optimal order of performing more complex shunting operations, such as sorting cars into several tracks, collecting cars on one track, train formation, and others.