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Optimization of fuzzy bi-objective fractional assignment problem

  • Neha GuptaEmail author
Application Article
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Abstract

Theory and applications of fractional programming have been significantly developed in the few last decades and assignment problem is one of the fundamental combinatorial optimization problems in the branch of optimization. Generally, in real world problems, the possible values of coefficients of a linear fractional programming problem are often only imprecisely or ambiguously known to the decision maker, therefore, it would be certainly more appropriate to interpret the coefficients as fuzzy numerical data. In this article, a fuzzy bi-objective fractional assignment problem has been formulated. Here the parameters are represented by triangular fuzzy numbers and the fuzzy problem is transformed into standard crisp problem through \(\alpha \)-cut and then the compromise solution is derived by fuzzy programming.

Keywords

Assignment problem Fractional programming problem Fuzzy numbers Fuzzy programming 

Notes

Acknowledgements

The author express their sincere thanks to editor and referees for their valuable suggestions and comments, which improved the quality of the paper.

References

  1. 1.
    Akkapeddi, S.M.: Fuzzy programming with quadratic membership functions for multi-objective transportation problem. Pak. J. Stat. Oper. Res. 11(2), 231–240 (2015)CrossRefGoogle Scholar
  2. 2.
    Bellman, R.E., Zadeh, L.A.: Decision-making in a fuzzy environment. Manag. Sci. 17(4), B-141 (1970)CrossRefGoogle Scholar
  3. 3.
    Charnes, A., Cooper, W.W.: Programming with linear fractional functionals. Naval Res. Logist. Q. 9(3–4), 181–186 (1962)CrossRefGoogle Scholar
  4. 4.
    De, P.K., Yadav, B.: A general approach for solving assignment problems involving with fuzzy cost coefficients. Mod. Appl. Sci. 6(3), 2 (2012)CrossRefGoogle Scholar
  5. 5.
    Dinkelbach, W.: On nonlinear fractional programming. Manag. Sci. 13, 492–498 (1967)CrossRefGoogle Scholar
  6. 6.
    Gupta, R.: Decomposition method and transportation type problems with a fractional objective function. ZAMM-J. Appl. Math. Mech. (Zeitschrift fr Angewandte Mathematik und Mechanik) 57(2), 81–88 (1977)CrossRefGoogle Scholar
  7. 7.
    Kar, S., Basu, K., Mukherjee, S.: Solution of generalized fuzzy assignment problem with restriction on costs under fuzzy environment. Int. J. Fuzzy Math. Syst. 4, 169–180 (2014)Google Scholar
  8. 8.
    Kumar, A., Gupta, A., Kaur, A.: Method for solving fully fuzzy assignment problems using triangular fuzzy numbers. World Acad. Sci. Eng. Technol. Int. J. Comput. Electr. Autom. Control Inf. Eng. 3(7), 1889–1892 (2009)Google Scholar
  9. 9.
    Kumar, P.S., Hussain, R.J.: A method for solving balanced intuitionistic fuzzy assignment problem. Int. J. Eng. Res. Appl. 4(3), 897–903 (2014)Google Scholar
  10. 10.
    Lin, C.J.: A simplex-based labelling algorithm for the linear fractional assignment problem. Optimization 64(4), 929–939 (2015)CrossRefGoogle Scholar
  11. 11.
    Lin, C.J., Wen, U.P.: A labeling algorithm for the fuzzy assignment problem. Fuzzy Sets Syst. 142(3), 373–391 (2004)CrossRefGoogle Scholar
  12. 12.
    Pandian, P., Kavitha, K.: A new method for solving fuzzy assignment problems. Ann. Pure Appl. Math. 1, 69–83 (2012)Google Scholar
  13. 13.
    Sadia, S., Gupta, N., Ali, Q.M.: Multiobjective capacitated fractional transportation problem with mixed constraints. Math. Sci. Lett. 5(3), 235–242 (2016)CrossRefGoogle Scholar
  14. 14.
    Sakawa, M., Nishizaki, I., Uemura, Y.: Interactive fuzzy programming for two-level linear and linear fractional production and assignment problems: a case study. Eur. J. Oper. Res. 135(1), 142–157 (2001)CrossRefGoogle Scholar
  15. 15.
    Saruwatari, Y., Shigeno, M., Matsui, T.: An algorithm for fractional assignment problems. Discrete Appl. Math. 56(2), 333–343 (1995)Google Scholar
  16. 16.
    Swarup, K.: Transportation technique in linear fractional functional programming. J. R. Naval Sci. Serv. 21(5), 256–260 (1966)Google Scholar

Copyright information

© Operational Research Society of India 2019

Authors and Affiliations

  1. 1.Faculty of Management SciencesAmity UniversityNoidaIndia

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