Optimal Value Determination Using Traditional and Newly Developed Methods for Initial Basic Feasible Solution of the Russell and Vogel’s Approximation Methods

The optimization of transportation problems is a fundamental problem of linear programming where the objective is to minimize the transportation costs of goods to different destinations. In this paper, we are exploring a case study for a manufacturing company to reduce rail and cargo ship transportation costs from three warehouse sources to five shipping destinations. The transportation problem was solved using Russell Approximation Method (RAM) and Vogel’s Approximation Method (VAM) for comparison, and subsequently checked for optimality through Transportation Simplex Method and Putcha-Bhuiyan Method (Putcha et al. in Proceedings of world congress in engineering (WCE) 2010, London, UK, 2010 [8]). Results show that transportation of goods by a combination of rails and ships rather than rail alone was more cost-effective and optimal. Usually, the Putcha-Bhuiyan Method has been proven to be the most efficient optimization method, however, with this specialized transportation problem, the Transportation Simplex Method provided the lowest cost calculations with lowest number of iterations for maximum efficiency.