IJCMP | A New Method to Solving Generalized Fuzzy Transportation Problem-Harmonic Mean Method

Indexing and Abstracting

A New Method to Solving Generalized Fuzzy Transportation Problem-Harmonic Mean Method

S. Senthil Kumar , P. Raja , P. Shanmugasundram , Srinivasarao Thota

International Journal of Chemistry, Mathematics And Physics(IJCMP), Vol-4,Issue-3, May - June 2020, Pages 51-56 , 10.22161/ijcmp.4.3.3

Download | Downloads : 8 | Total View : 1138

Abstract:

Transportation Problem is one of the models in the Linear Programming problem. The objective of this paper is to transport the item from the origin to the destination such that the transport cost should be minimized, and we should minimize the time of transportation. To achieve this, a new approach using harmonic mean method is proposed in this paper. In this proposed method transportation costs are represented by generalized trapezoidal fuzzy numbers. Further comparative studies of the new technique with other existing algorithms are established by means of sample problems.

Keywords:

Fuzzy Transportation Problem (FTP); Generalized Trapezoidal Fuzzy Number (GTrFN); Ranking function; Harmonic Mean Method (HMM).

References:

[1] Amarpreet Kaur, Amit Kumar, A new approach for solving fuzzy transportation problems using generalized trapezoidal fuzzy numbers, Applied soft computing, 12(3) (2012), 1201-1213.
[2] S. Chanas, W. Kolodziejckzy, A.A. Machaj, A fuzzy approach to the transportation problem, Fuzzy Sets and Systems 13 (1984), 211-221.
[3] S. Chanas, D. Kuchta, A concept of the optimal solution of the transportation problem with fuzzy cost coefficients, Fuzzy Sets and Systems 82(1996), 299-305.
[4] A. Charnes, W.W. Cooper, The stepping-stone method for explaining linear programming calculation in transportation problem, Management Science l(1954), 49-69.
[5] W.W.Charnes, cooper and A.Henderson, An introduction to linear programming Willey, New York, 1953,113.
[6] S.J. Chen, S.M. Chen, Fuzzy risk analysis on the ranking of generalized trapezoidal fuzzy numbers, Applied Intelligence 26 (2007), 1-11.
[7] S.M. Chen, J.H. Chen, Fuzzy risk analysis based on the ranking generalized fuzzy numbers with different heights and different spreads, Expert Systems with Applications 36 (2009), 6833-6842.
[8] G.B. Dantzig, M.N. Thapa, Springer: Linear Programming: 2: Theory and Extensions, Princeton University Press, New Jersey, 1963.
[9] D.S. Dinagar, K. Palanivel, The transportation problem in fuzzy environment, International Journal of Algorithms, Computing and Mathematics 2 (2009), 65-71.
[10] A. Edward Samuel, M. Venkatachalapathy, A new dual based approach for the unbalanced Fuzzy Transportation Problem, Applied Mathematical Sciences 6(2012), 4443-4455.
[11] A. Edward Samuel, M. Venkatachalapathy, A new procedure for solving Generalized Trapezoidal Fuzzy Transportation Problem, Advances in Fuzzy Sets and Systems 12(2012), 111-125.
[12] A. Edward Samuel, M. Venkatachalapathy, Improved Zero Point Method for Solving Fuzzy Transportation Problems using Ranking Function, Far East Journal of Mathematical Sciences,75(2013), 85-100.
[13] A. Gani, K.A. Razak, Two stage fuzzy transportation problem, Journal of Physical Sciences, 10 (2006), 63-69.
[14] F.L. Hitchcock, The distribution of a product from several sources to numerous localities, Journal of Mathematical Physics 20 (1941), 224-230.
[15] A. Kaufmann, M.M. Gupta, Introduction to Fuzzy Arithmetics: Theory and Applications, New York: Van Nostrand Reinhold, 1991.
[16] F.T. Lin, Solving the Transportation Problem with Fuzzy Coefficients using Genetic Algorithms, Proceedings IEEE International Conference on Fuzzy Systems, 2009, 20-24.
[17] T.S. Liou, M.J. Wang, Ranking fuzzy number with integral values, Fuzzy Sets and Systems 50 (1992), 247-255.
[18] S.T. Liu, C. Kao, Solving fuzzy transportation problems based on extension principle, European Journal of Operational Research 153 (2004), 661-674.
[19] G.S. Mahapatra, T.K. Roy, Fuzzy multi-objective mathematical programming on reliability optimization model, Applied Mathematics and Computation 174(2006), 643-659.
[20] P. Pandian, G. Natarajan, A new algorithm for finding a fuzzy optimal solution for fuzzy transportation problems, Applied Mathematical Sciences 4 (2010), 79- 90.
[21] N.V.Reinfeld and W.R.Vogel, Mathematical programming’’ Prentice – Hall, Englewood clifts, New jersey, (1958), 59-70.
[22] O.M. Saad, S.A. Abbas, A parametric study on transportation problem under fuzzy environment, The Journal of Fuzzy Mathematics 11 (2003), 115-124.
[23] L.A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338-353.
[24] H.J. Zimmermann, Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems 1 (1978), 45-55.