International Journal of Mathematics And Computer Research

Abstract

Reinfeld and Vogel (1958) developed a method known as Vogel’s Approximation Method (VAM), which has been the efficient solution procedure for more than sixty years, for obtaining an Initial Basic Feasible Solution (IBFS) for the transportation problems (TPs) as it provides a very good IBFS. The main notion of VAM is to determine penalty cost, which is the difference between the smallest cost and next to the smallest cost in each row and column and make maximum possible allocation at the least cost cell of that row or column which have the highest penalty. While determining the penalty cost the difficulty arises when the smallest and next to the smallest cost have the same identical values. Utpal Kant Das et al. (January 2014) resolved this difficulty and developed a new algorithm named Advanced Vogel’s Approximation Method (AVAM) to find an IBFS of TPs and showed that the AVAM gives the lower IBFS than that of by the VAM. During our research, we have identified some limitations of the algorithm of AVAM in selecting a row or column when two or more penalty costs have the same highest magnitude and also in selecting a cell for allocation when the smallest cost cell appears in two or more cells in the selected row or column. In this paper, we propose an effective improvement of AVAM in the solution procedure and named it as Revised version of AVAM (RAVAM) to obtain a better IBFS than AVAM for the TPs. To verify the performance of the proposed method, a comparative study is also carried out. Simulation results authenticate that RAVAM yields better IBFS in 90% of the cases than AVAM.