An Enhanced Vogel Approximation Method for Solving the TransportationProblem

The transportation problem is a classical linear programming model for allocating shipments from several supply points to several demand points at minimum total cost. A high-quality initial basic feasible solution is important because it can reduce the number of improvement iterations required by subsequent optimality tests. This study proposes an Enhanced Vogel Approximation Method (EVAM), a penalty-based modification of Vogel's Approximation Method that uses the three smallest active costs in each row or column. The method was tested on a balanced $5\times5$ transportation instance and compared with the Improved Vogel's Approximation Method (IVAM), followed by Stepping Stone improvement. The results show that IVAM produced an initial solution equal to the optimal cost of 59,356, whereas EVAM produced an initial cost of 60,727. After three Stepping Stone iterations, EVAM reached the same optimal cost of 59,356, with an initial optimality gap of 2.31\%. These findings indicate that EVAM is simple and transparent, although it does not dominate IVAM on the tested instance.