Most of the current methods for solving linear fractional programming (LFP) problems depend on the simplex type method. In this paper, we present a new approach for solving linear fractional programming problem in which the objective function is a linear fractional function, while constraint functions are in the form of linear inequalities. This approach does not depend on the simplex type method. Here first we transform this LFP problem into linear programming (LP) problem and hence solve this problem algebraically using the concept of duality. Two simple examples to illustrate our algorithm are given. And also we compare this approach with other available methods for solving LFP problems.
References
[1]
Charnes, A. and Cooper, W.W. (1962) Programming with Fractional Functions. Naval Research Logistic Quarterly, 9, 181-186. https://doi.org/10.1002/nav.3800090303
[2]
Bitran, G.R. and Novaes, A.G. (1973) Linear Programming with a Fractional Objective Functions. Operations Research, 21, 22-29. https://doi.org/10.1287/opre.21.1.22
[3]
Bitran, G.R. and Magnanti, T.L. (1976) Duality and Sensitivity Analysis with Fractional Objective Function. Journal of Operation Research, 24, 675-699. https://doi.org/10.1287/opre.24.4.675
[4]
Sing, H.C. (1981) Optimality Condition in Fractional Programming. Journal of Optimization Theory and Applications, 33, 287-294. https://doi.org/10.1007/BF00935552
[5]
Swarup, K. (1964) Linear Fractional Programming. Operation Research, 13, 1029-1036. https://doi.org/10.1287/opre.13.6.1029
[6]
Tantawy, S.F. (2008) A New Procedure for Solving Linear Fractional Programming Problems. Mathematical and Computer Modelling, 48, 969-973. https://doi.org/10.1016/j.mcm.2007.12.007
[7]
Tantawy, S.F. (2014) A New Concept of Duality for Linear Fractional Programming Problems. International Journal of Engineering and Innovative Technology, 3, 147-149.
[8]
Effati, S. and Pakdaman, M. (2012) Solving the Interval-Valued Linear Fractional Programming Problem. American Journal of Computational Mathematics, 5, 51-55. https://doi.org/10.4236/ajcm.2012.21006
[9]
Pramanik, S., Dey, P.P. and Giri, B.C. (2011) Multi-Objective Linear Plus Linear Fractional Programming Problem Based on Taylor Series Approximation. International Journal of Computer Applications, 32, 61-68.
[10]
Tantawy, S.F. (2008) An Iterative Method for Solving Linear Fractional Programming (LFP) Problem with Sensitivity Analysis. Mathematical and Computational Mathematics, 13, 147-151.
[11]
Tantawy, S.F. and Sallam, R.H. (2013) A New Method for Solving Linear Fractional Programming Problems. International Journal of Recent Scientific Research, 4, 623-625.