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Aim of this study is to determine the optimal cost for the given rectangular (or) square grid corresponding transportation problem along with balanced and unbalanced manner. We proposed the algorithmic way to provide cost from supply to the corresponding demand of the transportation problem in graph theoretical way to obtain minimum cost than the existed method in Operation Research. The proposed research brings out anoptimal basic feasible solution derived through graph theoretical method. It provides more than hundred percentage matching with so called existed method’s optimal basic feasible solution.
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