Author : Zahid Ali, Sayed Feroze Shah and Fozia Shaikh

In science, business and Mathematics is matrices are important tool which is used in almost all branches of
mathematics. Because the data is distributed in rows and columns by that arrangement, we can easily find out the
position of unit. So linear programming uses transportation problem like matrices and transportation problem is
very important tool for business in every aspect of life. Transportation problem plays vital role in business economy of every country to overcome the costs of goods. To solve balanced transportation problem there are many methods like LCM, NWCM and VAM are used to minimize the cost and maximize the profit. To overcome maximum transportation cost we use different means for balanced transportation problem to minimize the total cost of transportation problem that is initial basic feasible solution. The proposed algorithm gives better result than existing methods which are available for balanced transportation problems.

Keywords: Balanced transportation problem, Different means, Vogel approximation method, Arithmetic Mean, Geometric Mean, Harmonic Mean and Contra Harmonic Mean.

Article published in International Journal of Current Engineering and Technology, Vol.10, No.5 (Sept/Oct 2020)