Solving Multi-Objective Linear Fractional Programming Problem - First Order Taylor's Series Approximation Approach

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 246)


In this paper, a method is proposed for solving multi-objective linear fractional programming (MOLFP) problem. Here, the MOLFP problem is transformed into an equivalent multi-objective linear programming (MOLP) problem. Using the first-order Taylor's series approximation, the MOLFP problem is reduced to single-objective linear programming (LP) problem. Finally, the solution of MOLFP problem is obtained by solving the resultant LP problem. The proposed procedure is verified with the existing methods through the numerical examples.


Linear programming problem Multi-objective linear programming problem Taylor’s series 


  1. 1.
    H.I. Calvete, and C. Gale, “A penalty method for solving bilevel linear fractional programming/linear programming problems”, Asia-Pacific Journal of Operational Research 21, 207–224, 2004.Google Scholar
  2. 2.
    A. Charnes, and W.W. Cooper, W W, “Programming with linear fractional functionals”, Nav. Res. Logistics Quart. 9, 181–186, 1962.Google Scholar
  3. 3.
    M. Chakraborty, and S. Gupta, “Fuzzy mathematical programming for multi objective linear fractional programming problem”, Fuzzy Sets and Systems 125, 335–342, 2002.Google Scholar
  4. 4.
    J.P. Costa, “An interactive method for multiple objective linear fractional programming problems”, OR Spectrum, 27, 633–652, 2005.Google Scholar
  5. 5.
    W. Dinkelbach, “On nonlinear fractional programming”, Manage. Sci. 13, 492–498, 1967.Google Scholar
  6. 6.
    D. Dutta, R.N. Tiwari, and J.R. Rao, “Multiple objective linear fractional programming—A fuzzy set theoretic approach”, Fuzzy Sets and Systems 52, 39–45, 1992.Google Scholar
  7. 7.
    P.C. Gilmore, and R.E. Gomory, “A linear programming approach to the cutting stock problem. Part II”, Operational Research, 11, 863–888, 1963.Google Scholar
  8. 8.
    J.S.H. Kornbluth, and R.E. Steuer, “Goal programming with linear fractional criteria”, European J. Operational Research, 8, 58–65, 1981.Google Scholar
  9. 9.
    J.S.H. Kornbluth, and R.E. Steuer, “Multiple objective linear fractional programming”, Manage. Sci. 27, 1024–1039, 1981.Google Scholar
  10. 10.
    M.K. Luhandjula, “Fuzzy approaches for multiple objective linear fractional optimization”, Fuzzy Sets and Systems 13, 11–23, 1984.Google Scholar
  11. 11.
    S. Mishra, “Weighting method for bi-level linear fractional programming problems”, European Journal of Operational Research, 183, 296–302, 2007.Google Scholar
  12. 12.
    Neelam Malhotra and S.R. Arora, “An algorithm to solve linear fractional bi-level programming problem via goal programming”, OPSEARCH, 37, 1–13, 2000.Google Scholar
  13. 13.
    I. Nykowski, and Z. Zolkiewski, “A compromise procedure for the multiple objective linear fractional programming problem”, European Journal of Operational Research. 19, 91–97, 1985.Google Scholar
  14. 14.
    S. Schaible, “Fractional programming I: duality”, Manage. Sci. 22, 658–667, 1976.Google Scholar

Copyright information

© Springer India 2014

Authors and Affiliations

  1. 1.Department of Applied Mathematics and Computational SciencesPSG College of TechnologyCoimbatoreIndia

Personalised recommendations