A New Approach of Solving Linear Fractional Programming Problem (LFP) by Using Computer Algorithm
Affiliation(s)
1 Department of Applied Mathematics, Gono Bishwabidyalay (University), Dhaka, Bangladesh. 2 Department of Business Development, Allcare Limited, Dhaka, Bangladesh. 3 Department of Mathematics, University of Dhaka, Dhaka, Bangladesh. 4 Department of Mathematics, Jagannath University, Dhaka, Bangladesh.
1 Department of Applied Mathematics, Gono Bishwabidyalay (University), Dhaka, Bangladesh. 2 Department of Business Development, Allcare Limited, Dhaka, Bangladesh. 3 Department of Mathematics, University of Dhaka, Dhaka, Bangladesh. 4 Department of Mathematics, Jagannath University, Dhaka, Bangladesh.
ABSTRACT
In this paper, we study a new approach for solving linear fractional programming problem (LFP) by converting it into a single Linear Programming (LP) Problem, which can be solved by using any type of linear fractional programming technique. In the objective function of an LFP, if β is negative, the available methods are failed to solve, while our proposed method is capable of solving such problems. In the present paper, we propose a new method and develop FORTRAN programs to solve the problem. The optimal LFP solution procedure is illustrated with numerical examples and also by a computer program. We also compare our method with other available methods for solving LFP problems. Our proposed method of linear fractional programming (LFP) problem is very simple and easy to understand and apply.
In this paper, we study a new approach for solving linear fractional programming problem (LFP) by converting it into a single Linear Programming (LP) Problem, which can be solved by using any type of linear fractional programming technique. In the objective function of an LFP, if β is negative, the available methods are failed to solve, while our proposed method is capable of solving such problems. In the present paper, we propose a new method and develop FORTRAN programs to solve the problem. The optimal LFP solution procedure is illustrated with numerical examples and also by a computer program. We also compare our method with other available methods for solving LFP problems. Our proposed method of linear fractional programming (LFP) problem is very simple and easy to understand and apply.
Cite this paper
Saha, S. , Hossain, M. , Uddin, M. and Mondal, R. (2015) A New Approach of Solving Linear Fractional Programming Problem (LFP) by Using Computer Algorithm. Open Journal of Optimization, 4, 74-86. doi: 10.4236/ojop.2015.43010.
Saha, S. , Hossain, M. , Uddin, M. and Mondal, R. (2015) A New Approach of Solving Linear Fractional Programming Problem (LFP) by Using Computer Algorithm. Open Journal of Optimization, 4, 74-86. doi: 10.4236/ojop.2015.43010.
References
[1] Martos, B. (1960) Hyperbolic Programming, Publications of the Research Institute for Mathematical Sciences. Hungarian Academy of Sciences, 5, 386-407. [2] Martos, B. (1964) Hyperbolic Programming, Naval Research Logistics Quarterly, 11, 135-155.
http://dx.doi.org/10.1002/nav.3800110204 [3] Charnes, A. and Cooper, W.W. (1962) Programming with Linear Fractional Functions. Naval Research Logistics Quarterly, 9, 181-186.
http://dx.doi.org/10.1002/nav.3800090303 [4] Swarup, K. (1964) Linear Fractional Functional Programming. Operations Research, 13, 1029-1036.
http://dx.doi.org/10.1287/opre.13.6.1029 [5] Swarup, K., Gupta, P.K. and Mohan, M. (2003) Tracts in Operation Research. 11th Edition. [6] Bitran, G.R. and Novaes, A.J. (1973) Linear Programming with a Fractional Objective Function. Operations Research, 21, 22-29.
http://dx.doi.org/10.1287/opre.21.1.22 [7] Sing, H.C. (1981) Optimality Condition in Fractional Programming. Journal of Optimization Theory and Applications, 33, 287-294.
http://dx.doi.org/10.1007/BF00935552 [8] Tantawy, S.F. (2007) A New Method for Solving Linear Fractional Programming problems. Australian Journal of Basic and Applied Science, 1, 105-108. [9] Hasan, M.B. and Acharjee, S. (2011) Solving LFP by Converting It into a Single LP. International Journal of Operations Research, 8, 1-14. [10] Tantawy, S. (2008) An Iterative Method for Solving Linear Fraction Programming (LFP) Problem with Sensitivity Analysis. Mathematical and Computational Applications, 13, 147-151. [11] Effati, S. and Pakdaman, M. (2012) Solving the Interval-Valued Linear Fractional Programming Problem. American Journal of Computational Mathematics, 5, 51-55.
http://dx.doi.org/10.4236/ajcm.2012.21006 [12] 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.
[1] Martos, B. (1960) Hyperbolic Programming, Publications of the Research Institute for Mathematical Sciences. Hungarian Academy of Sciences, 5, 386-407. [2] Martos, B. (1964) Hyperbolic Programming, Naval Research Logistics Quarterly, 11, 135-155.
http://dx.doi.org/10.1002/nav.3800110204 [3] Charnes, A. and Cooper, W.W. (1962) Programming with Linear Fractional Functions. Naval Research Logistics Quarterly, 9, 181-186.
http://dx.doi.org/10.1002/nav.3800090303 [4] Swarup, K. (1964) Linear Fractional Functional Programming. Operations Research, 13, 1029-1036.
http://dx.doi.org/10.1287/opre.13.6.1029 [5] Swarup, K., Gupta, P.K. and Mohan, M. (2003) Tracts in Operation Research. 11th Edition. [6] Bitran, G.R. and Novaes, A.J. (1973) Linear Programming with a Fractional Objective Function. Operations Research, 21, 22-29.
http://dx.doi.org/10.1287/opre.21.1.22 [7] Sing, H.C. (1981) Optimality Condition in Fractional Programming. Journal of Optimization Theory and Applications, 33, 287-294.
http://dx.doi.org/10.1007/BF00935552 [8] Tantawy, S.F. (2007) A New Method for Solving Linear Fractional Programming problems. Australian Journal of Basic and Applied Science, 1, 105-108. [9] Hasan, M.B. and Acharjee, S. (2011) Solving LFP by Converting It into a Single LP. International Journal of Operations Research, 8, 1-14. [10] Tantawy, S. (2008) An Iterative Method for Solving Linear Fraction Programming (LFP) Problem with Sensitivity Analysis. Mathematical and Computational Applications, 13, 147-151. [11] Effati, S. and Pakdaman, M. (2012) Solving the Interval-Valued Linear Fractional Programming Problem. American Journal of Computational Mathematics, 5, 51-55.
http://dx.doi.org/10.4236/ajcm.2012.21006 [12] 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.