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The paper considers one of the methods of rounding a non-integer solution in the problem of optimal management of a fleet of railcars at a given time interval, which is reduced to solving a large-dimensional linear programming problem. There are a number of well-known methods for obtaining integer solutions or rounding methods that can be applied to an arbitrary linear programming problem, however, as is often the case, general methods are not always applicable to particular problems. Such tasks may require an individual approach, and the problem under consideration belongs to this type of tasks. The main limitation of the problem under consideration is its huge dimension, which in practice can reach several tens of millions of variables. The main idea of the presented approach is to obtain a non-integer solution at the first stage, then this solution is translated into the format of route chains, after which a new integer problem is solved, but already on the existing set of route chains. The new problem is characterized by a relatively small dimension and gives an integer answer no later than a few seconds.

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