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Complexity of the Operations Research Theory tasks can be often diminished incases that do not require finding the exact solution. For example, forecastingtwo-dimensional hierarchical time series leads us to the transportation problemwith a quadratic objective function and with additional constraints. Whilesolving this task there is no need to minimize objective function with highaccuracy, but it is very important to meet all the constraints. In this articlewe propose a simple iterative algorithm, which can find a valid transportationflow matrix in a limited number of steps while allowing massively parallelcomputing. Method's convergence was studied: a convergence criterion wasindicated, as well as the solution's accuracy estimation technique. It wasproved that the method converges with the speed of geometric progression, whoseratio weakly depends on the problem's dimension. Numerical experiments wereperformed to demonstrate the method's efficiency for solving specific largescale transportation problems.

A simple parallelizable method for the approximate solution of a quadratic transportation problem of large dimension with additional constraints