The optimization processes in mathematics, computer science and economics are solved effectively by choosing the best element from set of available alternatives elements. The most important and successful applications in the optimization refer to transportation problem, that is a special class of the linear programming in the operation research . The main objective of transportation problem solution methods is to minimize the cost or the time of transportation. Most of the currently used methods for solving transportation problems are trying to reach the optimal solution, whereby, most of these methods are considered complex and very expansive in term of the execution time. Finding an initial basic feasible solution is the prime requirement to obtain an optimal solution for the transportation problems. In this paper, a new method named minimum supply & demand method is proposed to find an initial basic feasible solution for the transportation problems. The method is also illustrated with numerical examples.

Transportation Problem(TP), Transportation Cost(TC), Initial Basic Feasible Solution (IBFS), Optimal Solution, Vogel’s approximation method(VAM), minimum supply & demand method (MSDM).

[1] V. Deshpande , “An Optimal method for Obtaining Initial Basic Feasible Solution of the Transportation Problem”, In National Conference on Emerging Trends in Mechanical Engineering, India , pp. 47-56, 2009.
[2] A. A. Hlayel, M. A. Alia, “ Solving Transportation PProblems Using The Best Candidates Method”,Computer Science & Engineering:
An International Journal (CSEIJ), Vol.2, Issue.5, pp.23-30, 2012.
[3] A. S.Soomro, G. A. Tularam, G.M. Bhayo, “A comparative study
of initial basic feasible solution methods for transportation
problems”, Mathematical Theory and Modeling,Vol.4 , Issue.1,
pp. 11-18, 2014.
[4] M. . Hakim, “An Alternative Method to Find Initial Basic Feasible
Solution of a Transportation Problem”, Annals of Pure and Applied
Mathematics, Vol. 1, Issue. 2, pp.203-209, 2012.
[5] A. Quddoos, S. Javaid, M. M. Khalid, “A New Method for Finding
an OptimalSolution for Transportation Problems” , International
Journal on Computer Science and Engineering , Vol. 4, Issue. 7,
pp.1271-1274, 2012.
[6] M.M. Ahmed, A.R.Khan, Md. S. Uddin, F. Ahmed, “A New
Approach to Solve Transportation Problems”, Open Journal of
Optimization, Vol.3 , Issue. 5, pp. 22-30, 2016.
[7] P.K.Gupta and M.Mohan, “ Problems in Operartions Research”, Sultan Chand & Sons Publisher , India, pp. 337 -400,1997.
[8] M. K. Hasan, “Direct Methods for Finding Optimal Solution of a Transportation Problem are not Always Reliable”, International Refereed Journal of Engineering and Science , Vol. 1, Issue. 2, pp.46-52, 2012.
[9] K. Jain, “Maximum Zero Method to Find Initial Basic Feasible
Solution of a Transportation Problem”, International Journal of
Applied Engineering Research, vol. 10, Issue.35 , pp.27542-27546,
2015.
[10] R.V.Joshi, “Optimization Techniques ,
[11] KAPOOR V. K., “Operations Research ( QuantitativeTechniques for management )”, Sultan Chand & Sons Publisher , pp. .5.3-5.97, India,
2008.
[12] K.Jain,S.Sood, “Maximum Zero Method to Find Initial Basic
Feasible Solution of a Transportation Problem”, International
Journal of Applied Engineering Research, Vol. 10, Issue.35,
pp.27542-27546, 2015.
[13] E. Hosseini, “Three New Methods to Find Initial Basic Feasible
Solution of Transportation Problems”, Applied Mathematical
Sciences, Vol. 11, Issue. 37, pp.1803 - 1814 , 2017.
[14] P.K.Gupta and D.S.Hira, “ Operartions Research”, Sultan Chand & Sons Publisher , India, pp. 148 -210,1997.
[15] S.D.Sharma , “ Operartions Research Thoery, Methods and Applications”, Kedar Nath Ram Nath & Co. , India, pp. 347 -434, 2003.