[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14317/jami.2011.29.3_4.831

APPLICATION OF LINEAR PROGRAMMING FOR SOLVING FUZZY TRANSPORTATION PROBLEMS

Kumar, Amit (School of Mathematics and Computer Applications, Thapar University)
Kaur, Amarpreet (School of Mathematics and Computer Applications, Thapar University)

Publication Information

Journal of applied mathematics & informatics / v.29, no.3_4, 2011 , pp. 831-846 More about this Journal

Abstract

There are several methods, in the literature, for finding the fuzzy optimal solution of fully fuzzy transportation problems (transportation problems in which all the parameters are represented by fuzzy numbers). In this paper, the shortcomings of some existing methods are pointed out and to overcome these shortcomings, a new method (based on fuzzy linear programming formulation) is proposed to find the fuzzy optimal solution of unbalanced fuzzy transportation problems with a new representation of trapezoidal fuzzy numbers. The advantages of the proposed method over existing method are discussed. Also, it is shown that it is better to use the proposed representation of trapezoidal fuzzy numbers instead of existing representation of trapezoidal fuzzy numbers for finding the fuzzy optimal solution of fuzzy transportation problems. To illustrate the proposed method a fuzzy transportation problem (FTP) is solved by using the proposed method and the obtained results are discussed. The proposed method is easy to understand and to apply for finding the fuzzy optimal solution of fuzzy transportation problems occurring in real life situations.

Keywords

Fuzzy sets; Linear programming; Ranking function; Trapezoidal fuzzy number; JMD trapezoidal fuzzy number;

Citations & Related Records

Reference

1	L.A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338-353. DOI
2	H.J. Zimmermann, Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems 1 (1978), 45-55. DOI ScienceOn
3	S.T. Liu and C. Kao, Solving fuzzy transportation problems based on extension principle, European Journal of Operational Research 153 (2004), 661-674. DOI ScienceOn
4	M. Oheigeartaigh, A fuzzy transportation algorithm, Fuzzy Sets and Systems 8 (1982), 235-243. DOI ScienceOn
5	P. Pandian, G. Natarajan, A new algorithm for finding a fuzzy optimal solution for fuzzy transportation problems, Applied Mathematical Sciences 4 (2010), 79-90.
6	O.M. Saad and S.A. Abbas, A parametric study on transportation problem under fuzzy environment, The Journal of Fuzzy Mathematics 11 (2003), 115-124.
7	T.S. Liou and M.J.Wang, Ranking fuzzy number with integral value, Fuzzy Sets and Systems 50 (1992), 247-255. DOI ScienceOn
8	A. Gani and K.A. Razak, Two stage fuzzy transportation problem, Journal of Physical Sciences 10 (2006), 63-69.
9	P. Gupta, and M.K. Mehlawat, An algorithm for a fuzzy transportation problem to select a new type of coal for a steel manufacturing unit, TOP 15 (2007), 114-137. DOI ScienceOn
10	F.L. Hitchcock, The distribution of a product from several sources to numerous localities, Journal of Mathematical Physics 20 (1941), 224-230.
11	D. Dubois, and H. Prade, Fuzzy Sets and Systems : Theory and Applications, Academic Press, New York, 1980.
12	S. Chanas, W. Kolodziejczyk and A.A Machaj, A fuzzy approach to the transportation problem, Fuzzy Sets and Systems 13 (1984), 211-221. DOI ScienceOn
13	S. Chanas and D. Kuchta, A concept of the optimal solution of the transportation problem with fuzzy cost coeffcients, Fuzzy Sets and Systems 82 (1996), 299-305. DOI ScienceOn
14	D.S. Dinagar, K. Palanivel, The transportation problem in fuzzy environment, International Journal of Algorithms, Computing and Mathematics 2 (2009), 65-71.