This paper focuses on new analytical solutions in the area of building locomotives’ circulation plans to handle individual applications for route transportation of freight. Such a domain has been little researched for the railway network of Ukraine, whereas the present study provides a basis for automating the planning process. The main aim is to improve the methods of determining the schemes of locomotives’ turnover in the railway network of Ukraine under the condition of an accelerated handling of individual railcar traffic and with regard to technological peculiarities. The developed mathematical model simultaneously makes it possible to determine the weight of trains on the routes they follow, to outline the circuity of locomotives with regard to deploying various series of locomotives within the network, and to regulate the system of locomotive crews’ operations in view of the existing technical and technological features of locomotive facilities and the railway infrastructure. The suggested mathematical model is processed in the study through the use of an integer genetic algorithm with its own system of coding the solution. The results have confirmed the adequacy of the developed mathematical model. The use of the suggested mathematical model on the basis of the genetic algorithm can help automate the complex process of determining the schemes of locomotives’ circulation with regard to the technological peculiarities of railcar traffic and, consequently, improve the accuracy and speed of decision-making for servicing individual applications for route transportation of freight.