An Attempt to Revamp Vogel’s Approximate Method for Optimality of Transportation Problems

Abstract

The transportation of products from manufacturers to destinations, while ensuring profitability, constitutes a pivotal facet of industrial operations. Nevertheless, the inherent unpredictability of transportation costs poses a challenge. Therefore, a linear programming is devised to mitigate overarching expenses. Solution of a transportation problem requires the initial feasible solution to get an optimal solution. Vogel’s Approximation Method, which is very effectual in the literature, however difficulty arises in the algorithm when two smallest costs have same magnitude. In that instance, this study aims to revamp Vogel’s method for balanced problems by employing a statistical approach to prevail over the difficulties of the Vogel Approximation Method (VAM) and to identify a feasible solution that is closer to the optimal solution than VAM. A range of literature examples have been investigated to validate the legitimacy and efficacy of the suggested algorithm. Additionally, the findings indicate significant achievements in cost reduction. The Initial Basic Feasible Solution of the revamped approach has been proven to be perfectly optimal, nearly optimal, equivalent to VAM, or superior to conventional methods.