Enhanced supply selection for better initial basic feasible solutions in transportation problems

The Transportation Problem (TP) is an optimization model that distributes goods from multiple supply points to various demand points at minimal cost. A crucial step in solving TP is generating an Initial Basic Feasible Solution (IBFS), which affects the efficiency of reaching the optimal solution. However, existing IBFS methods such as Supply Selection Method (SSM), Vogel's Approximation Method (VAM), Bilqis-Chastine-Erma (BCE). Juman-Hoque Method (JHM), and Total Opportunity Cost Matrix-Minimal Total (TOCM-MT) are not always reliable in producing low-cost solutions. This study proposes the Rihan-Bilqis-Saikhu Method (RBSM). This heuristic modifies SSM by considering the total cost-supply of each cell and adjusting how surplus allocations are shifted to rows with shortages. The method was evaluated using 42 test cases, including 32 published test cases, 5 randomly generated test cases, and 5 real test cases from XYZ company. Results show that RBSM outperformed all comparison methods, achieving the optimal solution in 36 out of 42 cases (85.71 % accuracy) and producing the lowest average deviation (0.58 %) from the optimal cost. The contributions of RBSM are:•Integration of total cost-supply into allocation decisions.•Refined reallocation rules between surplus rows and rows with shortages.•Consistent accuracy and efficiency across diverse test cases.