Overview of Optimality of New Direct Optimal Methods for the Transportation Problems

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. Original Research Article Jamali et al.; ARJOM, 15(4): 1-10, 2019; Article no.ARJOM.52506 2

[1]  Abraham Charnes,et al.  The Stepping Stone Method of Explaining Linear Programming Calculations in Transportation Problems , 1954 .

[2]  Veena Adlakha,et al.  Alternate Solutions Analysis For Transportation Problems , 2011 .

[4]  Asim Imdad Wagan,et al.  Numerical data concerning wind farm layout optimization using differential evolution algorithm at different wind speeds , 2017, Data in brief.

[5]  Asim Imdad Wagan,et al.  Power Optimization of Wind Turbines by the Adjoint Method , 2016 .

[6]  Asim Imdad Wagan,et al.  Application of Differential Evolution for Wind Turbine Micrositing , 2017 .

[7]  Hamdy A. Taha,et al.  Operations Research: An Introduction, 8/e , 2008 .

[8]  F. L. Hitchcock The Distribution of a Product from Several Sources to Numerous Localities , 1941 .

[9]  G. Geetharamani,et al.  An Innovative Method for Solving Fuzzy Transportation Problem , 2011 .

[10]  Asim Imdad Wagan,et al.  Wind turbine micrositing by using the firefly algorithm , 2015, Appl. Soft Comput..

[11]  Abdul Quddoos,et al.  A New Method for Finding an Optimal Solution for Transportation Problems , 2012 .

[12]  Asim Imdad Wagan,et al.  A New Hybrid Metaheuristic Algorithm for Wind Farm Micrositing , 2017 .

[13]  A. S. Soomro,et al.  On Non-Optimality of Direct Exponential Approach Method for Solution of Transportation Problems , 2017 .

[14]  Ömer Kirca,et al.  A Heuristic for Obtaining and Initial Solution for the Transportation Problem , 1990 .

[15]  Gurudeo Anand Tularam,et al.  A comparative study of initial basic feasible solution methods for transportation problems , 2014 .