Procedure for Solving Unbalanced Fuzzy Transportation Problem for Maximizing the Profit

  IJCOT-book-cover
 
International Journal of Computer & Organization Trends  (IJCOT)          
 
© 2015 by IJCOT Journal
Volume - 5 Issue - 2
Year of Publication : 2015
Authors :  S.krishna prabha, V.Seerengasamy
DOI : 10.14445/22492593/IJCOT-V18P305

Citation

S.krishna prabha, V.Seerengasamy"Procedure for Solving Unbalanced Fuzzy Transportation Problem for Maximizing the Profit", International Journal of Computer & organization Trends (IJCOT), V5(2):19-23 Mar - Apr 2015, ISSN:2249-2593, www.ijcotjournal.org. Published by Seventh Sense Research Group.

Abstract

A new method for maximizing profit in unbalanced transportation problems in fuzzy set theory is proposed. With the help of numerical example, the proposed method is illustrated; we use Fuzzy transportation to find the least transportation cost of some commodities through a capacitated network when the supply and demand of nodes and the capacity and cost of edges are represented as fuzzy numbers.

References

[1] A. Gani and K.A.Razak(2006):”Two stage fuzzy transportation problem” journal of physical sciences, pp 63-69.
[2] F.L. Hitchcock(1941): “The distribution of a product from several sources to numerous localities” journal of mathematical physics pp 224-230
[3] H.J. Zimmermann(1978):“fuzzy programming and linear programming with several objective functions” Fuzzy Sets and Systems pp 45-55
[4] O.M. Saad and S.A. Abbas(2003): “A parametric study on transportation problem under fuzzy environment” The Journal of Fuzzy Mathematics pp 115-124.
[5] A. Charnes, W. W. Cooper and A. Henderson, OAn introduction to Linear Programming, Wiley,New Work, (1953).
[6] G.B. Dantzig, Linear Programming and Extensions, Princeton University Press, NJ, (1963
[7] P. Pandian, G. Natarajan(2010): “A new algorithm for finding a fuzzy optimal solution for fuzzy transportation problem” Applied Mathematical science vol. 4 pp 79-90.
[8] N.Kishore and Anurag Jayswal, Prioritized goal programming formulation of an unbalanced transportation problem with budgetary constraints, Industrial Engineering Journal, 9 (2001) 16-19.
[9] P.Pandian and G. Natarajan, A new method for finding an optimal solution for transportation problems, International J. of Math. Sci. and Engg. Appls., 4 (2010) 59-65.
[10] P.Pandian and G.Natarajan, A new method for finding an optimal solution of fully interval integer transportation problems, Applied Mathematical Sciences, 4 (2010) 1819-1830.
[11] R.N. T iwa r i , S .Dha rmar a n d J . R . Rao, P r i o r i t y s t ruc t u r e in fuzzy Goal Programming, Fuzzy Sets and Systems, 19 (1986) 251-259
[12] Ringuset J.L.Rinks, D.B., “ Interactive solutions for the linear multi objective transportation problem”. European Journal of operational research 32 (1987). PP96-106.
[13] Bellman R.E., Zadeh L.A, “ Decision making in a fuzzy environment”, Management Sci. 17(1970). PP.141-164.
[14] Charnas S.Delgado.M., Verdegy J.L., Vila M.A., “Interval and fuzzy extension of classical transportation problems”, Transporting planning technol.17 (1993), PP.203-218.
[15] Lai Y.J., Hwang C.L., “Fuzzy Mathematical Programming methods and Application”, Springer, Berlin (1992)
[16] Nagoor Gani. A and Stephan Dinagar.D, : A note on linear programming in fuzzy Environment”, proc.Nat.Aca, Sci., India , Sect.A, Vol.79, pt.I (2009).
[17] Zadeh, L. A(1965): “Fuzzy sets, information and control” vol 8 pp 338-353.
[18] Maleki H.R., “Ranking functions and their applications to fuzzy linear programming”, for East J.Math. Sci. 4(2002), PP.283-301.
[19] Bit A.K., Biswal M.P., Alam S.S., “ Fuzzy programming approach to multi criteria decision making transportation problem”, Fuzzy sets and system 50 (1992). PP.135-142.
[20] Waiel F., Abd El – Wahed, “ A Multi objective transportation problem under fuzziness”, Fuzzy sels and systems 117 (2001). PP.27-33.

Keywords
Fuzzy numbers, trapezoidal fuzzy numbers, fuzzy Vogel’s approximation method.