  Complexity of the Operations Research Theory tasks can be often diminished in
cases that do not require finding the exact solution. For example, forecasting
two-dimensional hierarchical time series leads us to the transportation problem
with a quadratic objective function and with additional constraints. While
solving this task there is no need to minimize objective function with high
accuracy, but it is very important to meet all the constraints. In this article
we propose a simple iterative algorithm, which can find a valid transportation
flow matrix in a limited number of steps while allowing massively parallel
computing. Method's convergence was studied: a convergence criterion was
indicated, as well as the solution's accuracy estimation technique. It was
proved that the method converges with the speed of geometric progression, whose
ratio weakly depends on the problem's dimension. Numerical experiments were
performed to demonstrate the method's efficiency for solving specific large
scale transportation problems.
