Abstract
This paper presents a chance constrained programming approach to the problem of maximizing the ratio of two linear functions of decision variables which are subject to linear inequality constraints. The coefficient parameters of the numerator of the objective function are assumed to be random variables with a known multivariate normal probability distribution. A deterministic equivalent of the stochastic linear fractional programming formulation has been obtained and a subsidiary convex program is given to solve the deterministic problem.
Similar content being viewed by others
References
Bajalinov, E.B.: Linear Fractional Programming: Theory, Methods, Applications and Software. Kluwer, Dublin (2003)
Callahan, J.R., Bector, C.R.: Optimization with global stochastic functions. ZAMM. 55, 528–530 (1975)
Chandra, S., Gulati, T.R.: A duality theorem for a nondifferentiable fractional programming problem. Man. Sc. 23, 32–37, (1976)
Charnes, A., Cooper, W.W.: Deterministic equivalents for optimizing and satisfying under chance constraints. Oper. Res. 11, 18–39 (1963)
Gupta, S.K., Bector, C.R.: Nature of quotients, products and rational powers of convex (concave) like functions. Maths Student 63–67 (1968)
Gupta, S.N., Jain, R.K.: Stochastic fractional programming under chance constraints with random technology matrix. Acta Cienc. Indica. XIIm(3), 191–198 (1986)
Dantzig, G.B., Thapa, M.N.: Linear Programming 2: Theory and Extensions. Springer, New York (2003)
Infanger, G.: Planning under Uncertainty. Boyd and Fraser, Danvers (1994)
Martos, B.: The direct power of adjacet vertex programming methods. Man. Sc. 12, 241–252 (1965)
Sharma, I.C., Aggarwal, S.P.: Fractional programming in communication systems. Unternehmensforchung 14(2), 52–155 (1970)
Sinha, S.M.: A duality theorem on nonlinear programming. Man. Sc. 12, 385–390 (1966)
Swarup, K.: Linear fractional functionals programming. Oper. Res. 13, 1029–1036 (1965)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gupta, S.N. A Chance Constrained Approach to Fractional Programming with Random Numerator. J Math Model Algor 8, 357–361 (2009). https://doi.org/10.1007/s10852-009-9110-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10852-009-9110-8