A Cost Supply Method for Finding an Initial Basic Feasible Solution of the Transportation Problem

The Transportation Problem (TP) allocates shipments from multiple supply points to demand points at minimum cost. Solving the TP begins with an Initial Basic Feasible Solution (IBFS), which affects the Total Cost (TC). Widely used IBFS heuristics, such as Vogel’s Approximation Method (VAM), Juman–Hoque Method (JHM), Total Opportunity Cost Matrix–Minimal Total (TOCM-MT), Bilqis–Chastine–Erma (BCE), and the Supply Selection Method (SSM), cannot always deliver a low-cost starting solution. This study proposes the Cost-Supply Method (CSM). The key innovation of CSM is the formulation of the Cost- Supply (CS) variable. Unlike earlier approaches that treat cost and supply separately, CSM combines them to identify "high-impact" rows. Across 42 balanced test cases, CSM attained the highest accuracy (78.57%), defined as instances in which the IBFS matches the known optimal, and the lowest mean percentage deviation (0.87%) from the optimal cost. Compared with VAM, accuracy improved from 52.38% to 78.57%, and deviation dropped from 4.21% to 0.87%, indicating that CSM yields lower-cost starting solutions more consistently.