A Two-dimensional approach for finding solutions of nonlinear fractional programming problems

E.A. Youness, M.A. Maaty, H.A. Eldidamony


The problem of finding the minimum value of the objective function of the fractional programming problems has attracted considerable research and interest in many fields such as production planning, financial and corporate planning, health care and hospital planning, etc. In this paper, a two-dimensional approach for finding solutions of nonlinear fractional optimization problems is introduced. The proposed algorithm shows how to obtain a new point and a new direction in the feasible region that improves the solution process by choosing three initial points from the feasible region without any conditions. The proposed algorithm is based mainly upon parametric approach, which is easy to understand and apply. Illustrative examples are presented.

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Basiya K. Abdulrahim, (2014), On Extreme Point Quadratic Fractional Programming Problem, Applied Mathematical Sciences, 8 (6): 261 – 277.

Chandra S; Chandramoham M (1980), A note on integer linear fractional programming, Naval Re-search Logistics Quarterly, 27: 171-174.

Charnes and W.W. Cooper, (1962), Programming with linear fractional functional, Naval Research Lo-gistics Quarterly, 9: 181-186.

Dinkelbach, W., (1967), On Nonlinear Fractional Programming, Management Science, 13 (7): 492-498.

Frank, M., and Wolfe, P. (1956). An algorithm for quadratic programming, Naval Research Logistic Quarterly 3 (1-2): 95-110.

J.R. Isbell and W.H. Marlow, (1956), Atrition games, Naval Research Logistics Quarterly, 3: 1-99.

Jeflea, Antoneta, (2003), "A parametric study for solving nonlinear fractional problems", AnaleleŞtiinţi-fice ale Universităţii “Ovidius" Constanţa. Seria: Ma-tematică, 11 (2): 87-92. http://eudml.org/doc/125842.

O. L. Mangasarian, "Nonlinear fractional pro-gramming", J. Oper. Res. Soc. Japan 12 (1969), 1-10.

Martos, (1964), Hyperbolic programming, Naval Research Logistics Quarterly, 11:135-155.

Nejmaddin A. Suleiman, Maher A. Nawkhass, (2013), A New Modified Simplex Method to Solve Quadratic Fractional Programming Problem and Compared it to a Traditional Simplex Method by Us-ing Pseudoaffinity of Quadratic Fractional Func-tions,Applied Mathematical Sciences, 7 (76): 3749 – 3764.

Nejmaddin A. Suleiman, Maher A. Nawkhass, (2013), Solving quadratic fractional programming problem, International Journal of Applied Mathemat-ical Research, 2 (2): 303-309.

Rajendra, V., (1993), On Integer Fractional Lin-ear Programming, Operations Research Society of India, 30: 174-176.

Seshan CR, Tibekar VG, (1980), Algorithms for integer fractional programming, Journal of the Indi-an Institute of Science, Section B-Physical and Chemical Series 62: 9-16.

Swarupk, (1965), some aspects of linear frac-tional functionals programming, Australian Journal of Statistics 7: 90-104.

H. Wolf, (1985), "A parametric method for solv-ing the linear fractional programming problem", Op-erations Research 33:835-841.

P. Wolfe, (1959), the Simplex Method for Quad-ratic Programming Economics, 27:382-398.

E. A. Youness, M. A. Maaty, H.A. Didamony, (2016), A Two-dimensional approach for finding ap-proximated solutions of optimization problems, In-ternational Journal of Advanced Research 4(2): 1083-1090.


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