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PROPOSAL OF A SOLUTION TO FUZZY TRANSPORTATION PROBLEM USING FUZZY SET APPROACH

Year 2007, Issue: 013, 54 - 61, 15.06.2007

Nuran Güzel

Abstract

In the real world applications, frequently may be faced up with transportation problems that these quantities may not be known in precise manner. The supplies and demands may be uncertain due to some uncontrollable factors. In this study, we have presented an algorithm solving fuzzy transportation problem using membership functions of these fuzzy numbers when the unit shipping costs, the supply quantities and the demand quantities are fuzzy numbers. The proposed solution algorithm to fuzzy transportation problem yields optimal compromise solutions. To show the ability the proposed solution, the numerical example has been presented. The given example is solved using optimization software WINQSB [16].

Keywords

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References

  • [1]. R.E. Bellmann, L.A. Zadeh, Decision -Making in a fuzxy environment, Management Science 17 (1970), B141-B164.
  • [2]. J.Lai, C.L.Hwang, Fuzzy Mathematical Programming, Springer-Verlag, (1992), Berlin.
  • [3]. S.T.Liu, C.Kao, Solving fuzzy transportation problem based on extension principle, EuropeanJournal of Operational Research 153(2004) 661-674.
  • [4]. W.F. Abd El-Wahed, A multi-objective transportation problem under juzziness,Fuzzy Sets and Systems, 117(2001),27-33.
  • [5]. S.Kikuchi, A method to defuzzify the fuzzy number: transportation problem application, Fuzzy sets and Systems 116 (2000),3-9.
  • [6]. J .1.Ringuest, D.B.Rinks, Interactive solutions for the linear multiobjective transportation problem, Eur. J.Oper. Res.32 (1987),96-106.
  • [7]. S. Chanas, W. Kolodziejczyk, A.Machaj, Ajuzzy approach to the transportation problem, Fuzzy Sets and Systems, 13 (1984),211-221.
  • [8]. S. Chanas, D. Kuchta, Fuzzy integer transportation problem, Fuzzy Sets and Systems, 98(1998), 291-298.
  • [9]. H.-J. Zimmermann, Fuzzy Set Theory and Its Applications, third ed., Kluwer Academic Publishers, Norwell, MA,1996.
  • [10]. Y.J .Lai,C.L.Hwang, Fuzzy Multiple Objective Decision Making, Springer, 1996. [ll].H.Ishlbuchi, H. Tanaka, Multi Objective Programming in optimization of interval objective function, European Journal ofOperationai Research 48(1990), 219-225.
  • [12]. S.Chanas,on the interval approximation of a fuzzy number Fuzzy Sets and Systems, 122 (2001),353-356.
  • [13].A.Sengupta, T.P. Pai,D.Chakraborty, Interpretation of inequality constraints involving interval coefficients and a solution to interval linear programming, Fuzzy Sets and Systems, 119(2001),129-138.
  • [14].S.Chanas,juzzy Integer transportation problem, FSS, 98 (1998),291-298.
  • [15].M.L.Hussein, Complete Solutions of multiple objective transportation problem with possibilistic coefficients, FSS,93(3),(1998), 293-299.
  • [16]. Chang, Y-L, WinQSB, Version 1.0 for Windows, Wiley ,(2001).

PROPOSAL OF A SOLUTION TO FUZZY TRANSPORTATION PROBLEM USING FUZZY SET APPROACH

Year 2007, Issue: 013, 54 - 61, 15.06.2007

Nuran Güzel

Abstract

Gercek problemlerde, miktarlanrun kesin olarak bilinmedigi tasima problemleri ile sik sik karsilasihr. Mevcut stok ve talep miktarlan bazt kontrol edilemeyen etmenlerden dolayi belirsiz olabilir. Bu cahsrnada, birim tasima maliyetleri ile stok ve talep miktarlan bularuk sayilar oldugunda, bularuk sayilann iiyelik fonksiyonlanm kullanarak bularuk tasirna problemini cozen bir algoritma sunduk. Onerilen bu cozurn algoritmasinda, tasima probleminin optimal uygun cozumleri elde edildi. Onerilen cozumtln etkinligini gostermek icin, sayisal ornek verildi. Verilen ornek WINQSB[16] optimizasyon prograrru ile cozuldu.

Keywords

yok

References

  • [1]. R.E. Bellmann, L.A. Zadeh, Decision -Making in a fuzxy environment, Management Science 17 (1970), B141-B164.
  • [2]. J.Lai, C.L.Hwang, Fuzzy Mathematical Programming, Springer-Verlag, (1992), Berlin.
  • [3]. S.T.Liu, C.Kao, Solving fuzzy transportation problem based on extension principle, EuropeanJournal of Operational Research 153(2004) 661-674.
  • [4]. W.F. Abd El-Wahed, A multi-objective transportation problem under juzziness,Fuzzy Sets and Systems, 117(2001),27-33.
  • [5]. S.Kikuchi, A method to defuzzify the fuzzy number: transportation problem application, Fuzzy sets and Systems 116 (2000),3-9.
  • [6]. J .1.Ringuest, D.B.Rinks, Interactive solutions for the linear multiobjective transportation problem, Eur. J.Oper. Res.32 (1987),96-106.
  • [7]. S. Chanas, W. Kolodziejczyk, A.Machaj, Ajuzzy approach to the transportation problem, Fuzzy Sets and Systems, 13 (1984),211-221.
  • [8]. S. Chanas, D. Kuchta, Fuzzy integer transportation problem, Fuzzy Sets and Systems, 98(1998), 291-298.
  • [9]. H.-J. Zimmermann, Fuzzy Set Theory and Its Applications, third ed., Kluwer Academic Publishers, Norwell, MA,1996.
  • [10]. Y.J .Lai,C.L.Hwang, Fuzzy Multiple Objective Decision Making, Springer, 1996. [ll].H.Ishlbuchi, H. Tanaka, Multi Objective Programming in optimization of interval objective function, European Journal ofOperationai Research 48(1990), 219-225.
  • [12]. S.Chanas,on the interval approximation of a fuzzy number Fuzzy Sets and Systems, 122 (2001),353-356.
  • [13].A.Sengupta, T.P. Pai,D.Chakraborty, Interpretation of inequality constraints involving interval coefficients and a solution to interval linear programming, Fuzzy Sets and Systems, 119(2001),129-138.
  • [14].S.Chanas,juzzy Integer transportation problem, FSS, 98 (1998),291-298.
  • [15].M.L.Hussein, Complete Solutions of multiple objective transportation problem with possibilistic coefficients, FSS,93(3),(1998), 293-299.
  • [16]. Chang, Y-L, WinQSB, Version 1.0 for Windows, Wiley ,(2001).
There are 15 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Articles
Authors

Nuran Güzel

Publication Date June 15, 2007
Published in Issue Year 2007 Issue: 013

Cite

APA Güzel, N. (2007). PROPOSAL OF A SOLUTION TO FUZZY TRANSPORTATION PROBLEM USING FUZZY SET APPROACH. Journal of Science and Technology of Dumlupınar University(013), 54-61.
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