Fuzzy goal programming for multiobjective transportation problems

  • M. Zangiabadi
  • H. R. Maleki


Several fuzzy approaches can be considered for solving multiobjective transportation problem. This paper presents a fuzzy goal programming approach to determine an optimal compromise solution for the multiobjective transportation problem. We assume that each objective function has a fuzzy goal. Also we assign a special type of nonlinear (hyperbolic) membership function to each objective function to describe each fuzzy goal. The approach focuses on minimizing the negative deviation variables from 1 to obtain a compromise solution of the multiobjective transportation problem. We show that the proposed method and the fuzzy programming method are equivalent. In addition, the proposed approach can be applied to solve other multiobjective mathematical programming problems. A numerical example is given to illustrate the efficiency of the proposed approach.

AMS Mathematics Subject Classification

90C05 90C70 

Key words and phrases

Multiobjective decision making goal programming transportation problem membership function fuzzy programming 


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  1. 1.
    W. F. Abd El-Wahed and S. M. Lee,Interactive fuzzy goal programming for multi objective transportation problems, Omega34 (2006), 158–166.CrossRefGoogle Scholar
  2. 2.
    R. S. Aenaida and N. W. Kwak,A linear goal programming for transshipment problems with flexible supply and demand constraints, Journal of Operational Research Society45(2) (1994), 215–224.Google Scholar
  3. 3.
    A. K. Bit, M. P. Biswal and S. S. Alam,Fuzzy programming approach to multicriteria decision making transportation problem, Fuzzy Sets and Systems50 (1992), 135–141.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    A. K. Bit, M. P. Biswal and S. S. Alam,Fuzzy programming approach to multiobjective solid transportation problem, Fuzzy Sets and Systems57 (1993), 183–194.MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    A. K. Bit, M. P. Biswal and S. S. Alam,An additive fuzzy programming model for mul tiobjective transportation problem, Fuzzy Sets and Systems57 (1993), 313–319MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    S. Chanas and D. Kuchta,A concept of the optimal solution of the transportation problem with fuzzy cost coefficients, Fuzzy Sets and Systems82 (1996), 299–305.CrossRefMathSciNetGoogle Scholar
  7. 7.
    S. Chanas and D. Kuchta,Fuzzy integer transportation problem, Fuzzy Sets and Systems98 (1998), 291–298.CrossRefMathSciNetGoogle Scholar
  8. 8.
    S. Chanas, W. Kolodziejckzy and A. A. Machaj,A fuzzy approach to the transportation problem, Fuzzy Sets and Systems13 (1984), 211–221.MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    A. Charnes and W. W. Cooper,Management Models of Industrial Applications of Linear Programming (Appendix B), Vol. I, Wiley, New York, 1961.Google Scholar
  10. 10.
    M. Ehrgott and R. A. Verma,Note on solving multicriteria transportationlocation prob lems by fuzzy programming, Asia-Pacific Operational Research18 (2001), 149–164.MATHMathSciNetGoogle Scholar
  11. 11.
    E. L. Hannan,Linear programming with multiple fuzzy goals, Fuzzy Sets and Systems6 (1981), 235–248.MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    E. L. Hannan,On fuzzy goal programming, Decision Sci.12 (1981), 522–531.CrossRefGoogle Scholar
  13. 13.
    J. P. Ignizio,Goal Programming and Extensions, Lexington D.C. Health, MA, 1976.Google Scholar
  14. 14.
    F. Jimenez and J. L. Verdegay,Solving fuzzy solid transportation problems by an evolu tionary algorithm based parametric approach, European J. Oper. Res.117 (1999), 485–510.MATHCrossRefGoogle Scholar
  15. 15.
    H. Leberling,On finding compromise solutions for multicriteria problems using the fuzzy minoperator, Fuzzy Sets and Systems6 (1981), 105–118.MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    S. M. Lee and L. J. Moore,Optimizing transportation problems with multiple objectives, AIEE Transactions5 (1973), 333–338.Google Scholar
  17. 17.
    L. Li and K. K. Lai,A fuzzy approach to the multiobjective transportation problem, Computers and Operational Research28 (2000), 43–57.CrossRefMathSciNetGoogle Scholar
  18. 18.
    M. Mishmast Nehi, H. R. Maleki and M. Mashinchi,A canonical representation for the solution of fuzzy linear system and fuzzy linear programming problem, J. Appl. Math. & Computing20(1-2) (2006), 345–354.MATHMathSciNetGoogle Scholar
  19. 19.
    R. H. Mohamed,The relationship between goal programming and fuzzy programming, Fuzzy Sets and Systems89 (1997), 215–222.CrossRefMathSciNetGoogle Scholar
  20. 20.
    R. Narasimhan,Goal programming in a fuzzy environment, Decision Sci.11 (1980), 325–336.CrossRefMathSciNetGoogle Scholar
  21. 21.
    B. B. Pal, B. N. Moitra and U. Maulik,A goal programming procedure for fuzzy multiob jective linear programming problem, Fuzzy Sets and Systems139 (2003), 395–405.MATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    M. Sakawa,Fuzzy sets and interactive multiobjective optimization, Plenum Press, New York, 1993.MATHGoogle Scholar
  23. 23.
    M. Tamiz, D. F. Jones and C. Romero,Goal programming for decision making an overview of the current state of the art, European Journal of Operational Research111 (1998), 569–581.MATHCrossRefGoogle Scholar
  24. 24.
    R. N. Tiwari, S. Dharmar and J. R. Rao,Fuzzy goal programming: an additive model, Fuzzy Sets and Systems24 (1987), 27–34.MATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    R. Verma, M. P. Biswal and A. Biswas,Fuzzy programming technique to solve multi objective transportation problem with some nonlinear membership functions, Fuzzy Sets and Systems91 (1997), 37–43.MATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    M. A. Yaghoobi and M. Tamiz,A short note on relationship between goal programming and fuzzy programming for vectormaximum problems, Iranian Journal of Fuzzy Systems2 (2005), 31–36.MATHMathSciNetGoogle Scholar
  27. 27.
    L. A. Zadeh,Fuzzy sets, Inform. and Control8 (1965), 338–353.MATHCrossRefMathSciNetGoogle Scholar
  28. 28.
    H. J. Zimmermann,Description and optimization of fuzzy systems, Int. J. General Systems2 (1976), 209–215.CrossRefGoogle Scholar
  29. 29.
    H. J. Zimmermann,Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems1 (1978), 45–55.MATHCrossRefMathSciNetGoogle Scholar
  30. 30.
    H. J. Zimmermann,Application of fuzzy set theory to mathematical programming, Information Sciences36 (1985), 29–58.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Korean Society for Computational & Applied Mathematics and Korean SIGCAM 2007

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer SciencesKerman UniversityKermanIran
  2. 2.Department of Basic SciencesShiraz University of TechnologyShirazIran

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