Overview of Optimality of New Direct Optimal Methods for the Transportation Problems
Sanaullah Jamali
University of Sindh, Laar Campus, Badin, Sindh, Pakistan.
Muhammad Mujtaba Shaikh *
Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro, Pakistan and Supply Chain and Operations Management Research Group, Mehran University of Engineering and Technology, Jamshoro, Pakistan.
Abdul Sattar Soomro
Institute of Mathematics and Computer Science, University of Sindh, Jamshoro, Sindh, Pakistan.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we investigate the claimed optimality of a new method – Revised Distribution (RDI) Method – for finding optimal solution of balanced and unbalanced transportation models directly and compare the RDI method with other such methods. A large set of problems have been tested by RDI and other methods, and the results were compared with the Modified distribution (MODI) method – an optimal method. We found that the mostly the results of RDI are not optimal. For reference to prove our observations, we have added three example transportation problems here in this work and compared their results with MODI method to show that the RDI method like the direct exponential approach (DEA) method is not optimal method; but it is just an initial basic feasible solution (IBFS) for transportation problems.
Keywords: Transportation problem, direct method, revised distribution, MODI method, optimality, non-optimal solution