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We propose a new method for solving transportation problems based on decomposing the original problem into a number of two-dimensional optimization problems. Since the solution procedure is integer-valued and monotonic in the objective function, the required computation is finite. As a result, we get not only a single optimal solution of the original transportation problem but a system of constraints that can yield all optimal solutions. We give numerical examples that illustrate the constructions of our algorithm.
Тизик et al. (Sun,) studied this question.