Mathematical formulation of new IBFS technique in comparison with VAM for solving a transportation problem

Abstract

This study is an extension of the research initiated by Somani (2015), to improve the Initial Basic Feasible Solution (IBFS) of a transportation problem (TP). The results of this new IBFS technique were compared to the Somani Approximation Method (SAM) and the well-known Vogel’s Approximation Method (VAM), using two literature values adopted in the study. From the analysis of the basic feasible solutions from the three methods in relation to the first literature data: the IBFS values of the given problem obtained from SAM, VAM and the new IBFS method were 555, 303 and 267 respectively. The corresponding results from the Modified Distribution (MODI) method on the IBFS of SAM, VAM and the new IBFS method also yielded an optimal solution value of 267. The total iterations involved in computing IBFS through to the optimal solution for SAM, VAM and the new IBFS method were 8, 6 and 4 respectively. In the second literature data, the IBFS values of the given transportation problem obtained from SAM, VAM and the new IBFS method were also 640, 625 and 625 respectively. Applying the MODI method on the IBFS of SAM, VAM and the new IBFS method provided an optimal solution value of 625. The total iterations involved in computing IBFS through to the optimal solution for SAM, VAM and the new IBFS method were 6, 4 and 4 respectively. Comparatively, the results from the study, aside from optimal solution obtained from fewer iterations, showed that the new IBFS Technique produces an IBFS value that is better than the one produced by either the SAM or the VAM. It is recommended that the new IBFS technique will be adopted by companies and businesses to solve their transportation problems.