the formulated problem is a special case of the transportation problem with xed surcharges in which the value of the objective function affect only the time spent on the delivery of resources by the affected routes and do not affect the volumes of transported resources. A solution based on the linearization of the objective function is appropriate in cases of time constraints on finding a solution. Second, because of its relative simplicity, this solution can be used as a duplicate procedure (to determine the lower limit) to more complex, such as, combinatorial, algorithms for finding exact solution of the problem. Modification of the method of Balinsky is the sequential reduction of dimensionality of the original problem by eliminating rows or columns of the matrix of transportation in which the true costs match the costs of these tasks

Keywords: transportation problem, the minimum total time, linearization of the objective function, the method of Balinsky