An Approach for Solving Linear Fractional Programming Problems
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Abstract
Linear fractional programming problems are useful tools in production planning, financial and corporate planning, health care and hospital planning and as such have attracted considerable research interest. The paper presents a new approach for solving a fractional linear programming problem in which the objective function is a linear fractional function, while the constraint functions are in the form of linear inequalities. The approach adopted is based mainly upon solving the problem algebraically using the concept of duality and partial fractions and an example is given to clarify the developed method.
References
[1] A.O. Odior, “Mathematics for Science and Engineering Students”, Vol.1, 3rd. Edition, Ambik Press, Benin City, Nigeria, (2003).
[2] S.F. Tantawy, “A New Method for Solving Linear Fractional Programming Problems”, Australian Journal of Basic and Applied Sciences, Vol. 1, No. 2, (2007), pp.105-108.
[3] A. Chaners and W.W. Cooper, “Programming with Linear Fractional Functionals” Naval Research Logistics Quarterly, Vol. 9, No 3-4, (1962), pp. 181-186.
[4] G. R. Bitran and A.J. Novaes, “Linear programming with a fractional objective function”, Journal of Operations Research, Vol 21 , No 4, (1973), pp: 22-29.
[5] G. R. Bitran and T.L. Magnanti, “Duality and Sensitivity Analysis with Fractional Objective Function” Journal of Operations Research, Vol 24, (1976), pp: 675-699.
View more references (12)
[6] L. Gwo-Liang and H. S. Shey, “Economic production quantity model for randomly failing production process with minimal repair and imperfect maintenance”, International Journal of Production Economics, Vol. 130, (2011), pp. 118–124.
[7] M. Chakraborty and S. Gupta, “Fuzzy mathematical programming for multi objective linear fractional programming problem. Fuzzy Set Syst., Vol.125, (2002), pp. 335–342
[8] D. Dutta, J. R. Rao and R. N.Taiwari, A restricted class of multi objective linear programming problems. European Journal of Operational Research, Vol. 68, (1993), 352-355.
[9] D. Dutta, J. R. Rao and R. N.Taiwari, “Fuzzy approaches for multiple criteria linear fractional optimization: a comment”, Fuzzy Sets and Systems Journal, Vol. 54, (1993), 347-349.
[10] D. Dutta, J. R. Rao and R. N.Taiwari, “Fuzzy approaches for multiple criteria linear fractional optimization: a comment, fuzzy set theoretic approach. Fuzzy Sets and Systems Journal, Vol.52, (1992), pp. 39-45.
[11] M.K. Luhandjula, “Fuzzy approaches for multiple objective linear fractional optimization” Fuzzy Set and System Journal, Vol. 13, (1984), pp. 11–23
[12] I. Nykowski.and Z. Zolkiewski, “A compromise producer for the multi objective linear fractional programming problem. Journal of Operations Research, Vol. 19, (1985), pp. 91-97.
[13] A. Azar, D. Andalib and S. H. Mirfakhroddini, “Production planning modeling: A fuzzy multi objective fractional programming approach, African Journal of Business Management Vol. 6, No.15, (2012), pp. 5288-5298.
[14] J. Rezaei and M. Davoodi, “Multi-objective models for lot-sizing with supplier selection. International Journal of Production Economics, Vol.130, (2011), pp. 77–86
[15] A. Chaudhuri and K. De, “Fuzzy multi-objective linear programming for travelling salesman problem’ African Journal of Mathematics and Computer Science Research, Vol.4, No.2, (2011), pp. 64- 70.
[16] J. S. H. Kornbluth and R. E. Steuer, “Multiple Linear Fractional Programming, Journal of Management science”, Vol.27, (1987), pp.1024- 1039.
[17] H . P. Benson, “Finding Certain Weakly–Efficient Vertices in Multiple Objective Linear Fractional Programming, Journal of Management Science, Vol.31, (1985), pp. 240-245.