Total opportunity cost matrix - Minimal total: A new approach to determine initial basic feasible solution of a transportation problem

Transportation Problem (TP) deals with cost planning for delivering the product from the source to the destination and Initial Basic Feasible Solution (IBFS) is presented to find the way out in obtaining an optimal solution. IBFS is an important element to reach an optimal result. The previous methods related to it did not always provide the satisfied result all the time. Therefore a new method called Total Opportunity Cost Matrix - Minimal Total (TOCM-MT) to determine IBFS as a basic solution to solve TP was proposed. The objective is to achieve a total cost with similar or closer values to the optimal solution. TOCM for the initial matrix and a better mechanism are highly considered to obtain IBFS. Thirty-one numerical examples, in which twenty-five were selected from some journals and six were generated randomly, were used to evaluate the performance of it. The proposed method has been compared to Vogel's Approximation Method (VAM), Juman and Hoque Method OHM), and Total Differences Method 1 (TDM1). TOCM-MT was proven to have twenty-four numerical examples with similar values and seven numerical examples with closer values to the optimal solution. The experiment results indicated that TOCM-MT obtained better minimal cost than that of VAM, JHM, and TDM1. (C) 2019 Production and hosting by Elsevier B.V. on behalf of Faculty of Computers and Information, Cairo University.