Research ArticleOpen AccessGoogle Scholar indexed
Solving the Interval-Valued Linear Fractional Programming Problem
Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
- 1 Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
- 2 Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
American Journal of Computational Mathematics·Volume 02 (2012)·Pages 51–55·Published 21 March 2012·DOI10.4236/ajcm.2012.21006
Copy link · social · email
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.
KeywordsInterval-Valued FunctionLinear Fractional ProgrammingInterval-Valued Linear Fractional Programming
- 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
- I. M. Stancu-Minasian, “Stochastic Programming with Multiple Ob-jective Functions,” D. Reidel Publishing Company, Dordrecht, 1984.
- I. M. Stancu-Minasian and St. Tigan, “Multiobjective Mathematical Programming with Inexact Data,” Kluwer Academic Publishers, Boston, 1990, pp. 395-418.
- 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
- 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
- I. M. Stancu-Minasian, “Fractional Programming,” Kluwer Academic Publishers, Dordrecht, 1997.
- 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
- 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
- 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
- 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
- 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
- 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.
- 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