Solving the Interval-Valued Linear Fractional Programming Problem

DOI: 10.4236/ajcm.2012.21006   PDF   HTML   XML   6,449 Downloads   13,323 Views   Citations

Abstract

This paper introduces an interval valued linear fractional programming problem (IVLFP). An IVLFP is a linear frac-tional programming problem with interval coefficients in the objective function. It is proved that we can convert an IVLFP to an optimization problem with interval valued objective function which its bounds are linear fractional functions. Also there is a discussion for the solutions of this kind of optimization problem.

Share and Cite:

S. Effati and M. Pakdaman, "Solving the Interval-Valued Linear Fractional Programming Problem," American Journal of Computational Mathematics, Vol. 2 No. 1, 2012, pp. 51-55. doi: 10.4236/ajcm.2012.21006.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] H. Ohta and T. Yamaguchi, “Linear Fractional Goal Programming in Consideration of Fuzzy Solution,” European Journal of Operational Research, Vol. 92, No. 1, 1996, pp. 157-165. doi:10.1016/0377-2217(95)00052-6
[2] I. M. Stancu-Minasian, “Stochastic Programming with Multiple Ob-jective Functions,” D. Reidel Publishing Company, Dordrecht, 1984.
[3] I. M. Stancu-Minasian and St. Tigan, “Multiobjective Mathematical Programming with Inexact Data,” Kluwer Academic Publishers, Boston, 1990, pp. 395-418.
[4] H.-C. Wu, “The Karush-Kuhn-Tucker Optimality Conditions in an Optimization Problem with Interval-Valued Objective Function,” European Journal of Operational Research, Vol. 176, No. 1, 2007, pp. 46-59. doi:10.1016/j.ejor.2005.09.007
[5] H.-C. Wu, “On Inter-val-Valued Nonlinear Programming Problems,” Journal of Mathematical Analysis and Applications, Vol. 338, No. 1, 2008, pp. 299-316. doi:10.1016/j.jmaa.2007.05.023
[6] I. M. Stancu-Minasian, “Fractional Programming,” Kluwer Academic Publishers, Dordrecht, 1997.
[7] A. Charnes and W. W. Cooper, “Pro-grams with Linear Fractional Functions,” Naval Research Lo-gistics Quarterly, Vol. 9, No. 3-4, 1962, pp. 181-196. doi:10.1002/nav.3800090303
[8] G. R. Bitran and A. G. No-vaes, “Linear Programming with a Fractional Function,” Op-erations Research, Vol. 21, No. 1, 1973, pp. 22-29. doi:10.1287/opre.21.1.22
[9] S. F. Tantawy, “A New Procedure for Solving Linear Fractional Programming Problems,” Mathematical and Computer Modelling, Vol. 48, No. 5-6, 969-973, 2008. doi:10.1016/j.mcm.2007.12.007
[10] P. Pandey and A. P. Punnen, “A Simplex Algorithm for Piecewise-Linear Fractional Programming Problems,” European Journal of Operational Research, Vol. 178, No. 2, 2007, pp. 343-358. doi:10.1016/j.ejor.2006.02.021
[11] H. Jiao, Y. Guo and P. Shen, “Global Optimization of Generalized Linear Fractional Programming with Non- linear Constraints,” Applied Mathe-matics and Computation, Vol. 183, No. 2, 2006, 717-728. doi:10.1016/j.amc.2006.05.102
[12] S. Schaible, “Analyse und Anwendungen von Quotientenprogrammen, Ein Beitrag zur Planung mit Hilfe der nichtlinearen Programmierung,” Mathe-matical Systems in Economics, Vol. 42, Hain-Verlag, Meisen-heim, 1978.
[13] S. Schaible, “Fractional Programming: Applications and Algorithms,” European Journal of Operational Research, Vol. 7, No. 2, 1981, pp. 111-120. doi:10.1016/0377-2217(81)90272-1
[14] S. Schaible and T. Ibaraki, “Fractional Programming, Invited Review,” European Journal of Operational Research, Vol. 12, No. 4, 1983, pp. 325-338. doi:10.1016/0377-2217(83)90153-4
[15] D. Ratz, “On Extended Interval Arithmetic and Inclusion Isotonicity,” Institut fur Angewandte Mathematik, University Karlsruhe, 1996.
[16] T. Hickey, Q. Ju and M. H. Van Emden, “Interval arithmetic: From Principles to Implementation,” Journal of the ACM, Vol. 48, 2001, pp. 1038-1068.
[17] S. F. Tantawy, “An Iterative Method for Solving Linear Fraction Programming (LFP) Problem with Sensitivity Analysis,” Mathematical and Computational applications, Vol. 13, No. 3, 2008, pp. 147-151.

  
comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.