Total opportunity cost matrix - Supreme cell: A new method to obtain initial basic feasible solution of transportation problems

Transportation Problem (TP) is delivering the product from supply to demand proposed to determine the minimal total cost. Initial Basic Feasible Solution (IBFS) is a foundation to find an optimal solution of TP. The previous methods did not provide optimal solution all the time. Therefore, in this paper, a new method called Total Opportunity Cost Matrix - Supreme Cell (TOCM-SC) was proposed to get better IBFS. This study aimed to achieve a minimal total as the optimal solution of TP. TOCM-SC can have a better result compared with other methods; since this method initializes the original matrix into the TOCM and starts with the cell, which has the highest supreme value. Twenty-three numerical examples selected from some journals were used to evaluate the performance of TOCM-SC. The proposed method, TOCM-SC, has been compared to other Initial Basic Feasible Solutions namely: Incessant Allocation Method (IAM), Vogel's Approximation Method (VAM), and Total Differences Method 1 (TDM1). The results of experiment show that TOCM-SC obtained better minimal cost than IAM, VAM, and TDM1. TOCM-SC achieved the optimal solution for seventeen of Twenty-three numerical examples with 73.91% accuracy.