THE MINIMUM DEMAND METHOD – A NEW AND EFFICIENT INITIAL BASIC FEASIBLE SOLUTION METHOD FOR TRANSPORTATION PROBLEMS

It is one of the most important tasks to determine the optimal solution for large scale transportation problems in Operations research more efficiently, accurately and quickly. In this research, we develop a new and efficient initial basic feasible solution (IBFS) method for solving balanced and unbalanced transportation problems so that the cost associated with transporting a certain amount of products from sources to destinations is minimized while also satisfying constraints. The proposed method – the minimum demand method (MDM) – to find a starting (initial) solution for the transportation problems has been developed by taking minimum value in demand row, and in case of a tie the demand with the least cost in the corresponding column is selected. The performance evaluation of the proposed MDM is carried out with other benchmark methods in the literature, like the north-westcorner method (NWCM), least cost method (LCM), Vogel’s approximation method (VAM) and revised distribution (RDI) method. The IBFSs obtained by the proposed MDM and existing NWCM, LCM, VAM and RDI have been compared against the optimal solutions acquired through the modified distribution (MODI) method on 12 balanced and unbalanced problems from literature, and the relative error distributions are presented for accuracy. The results obtained by the proposed MDM are better than NWCM, LCM, VAM and RDI. The proposed MDM gives initial basic feasible solutions that are the same as or very closer to the optimum solutions in all cases we have discussed. The comparison reveals that the proposed MDM reduces the number of tables and the number of iterations to reach at more accurate and reliable IBFS. The MDM will also save the total time period of performing tasks and reduce the number of steps in order to get the optimal solution. JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES www.journalimcms.org ISSN (Online) : 2454 -7190 Vol.-15, No.-10, October (2020) pp 94-109 ISSN (Print) 0973-8975 J. Mech. Cont.& Math. Sci., Vol.-15, No.-10, October (2020) pp 94-109 Sanaullah Jamali et al 95