This paper considers the problem of optimal management of a fleet of freight cars by a transport railway operator. The solution to this problem is an optimal plan, which is a timetable for the movement of freight and empty railway cars, following which the transport operator will receive the maximum profit for the estimated period of time. This problem is reduced to the problem of linear programming of large dimension. Unlike the works of other authors on this topic, which mainly deal with methods of numerical solution of the corresponding linear programming problems, this article focuses on an algorithm that allows one to reduce their dimensionality. This can be achieved by excluding from the calculation those routes that obviously cannot be involved in the solution, or whose probability of participation in the final solution is estimated as extremely low. The effectiveness of the proposed modified algorithm was confirmed both on a model example (several stations, a short planning horizon) and on a real example (more than 1.000 stations, a long planning horizon). In the first case, there was a decrease in the dimension of the problem by 44%, while in the second – by 30 times.