A Chance Constrained Approach to Fractional Programming with Random Numerator

  • S. N. GuptaEmail author


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.


Stochastic programming Chance constraint Linear fractional programming Multivariate normal distribution Deterministic equivalent 


  1. 1.
    Bajalinov, E.B.: Linear Fractional Programming: Theory, Methods, Applications and Software. Kluwer, Dublin (2003)zbMATHGoogle Scholar
  2. 2.
    Callahan, J.R., Bector, C.R.: Optimization with global stochastic functions. ZAMM. 55, 528–530 (1975)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Chandra, S., Gulati, T.R.: A duality theorem for a nondifferentiable fractional programming problem. Man. Sc. 23, 32–37, (1976)zbMATHMathSciNetGoogle Scholar
  4. 4.
    Charnes, A., Cooper, W.W.: Deterministic equivalents for optimizing and satisfying under chance constraints. Oper. Res. 11, 18–39 (1963)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Gupta, S.K., Bector, C.R.: Nature of quotients, products and rational powers of convex (concave) like functions. Maths Student 63–67 (1968)Google Scholar
  6. 6.
    Gupta, S.N., Jain, R.K.: Stochastic fractional programming under chance constraints with random technology matrix. Acta Cienc. Indica. XIIm(3), 191–198 (1986)MathSciNetGoogle Scholar
  7. 7.
    Dantzig, G.B., Thapa, M.N.: Linear Programming 2: Theory and Extensions. Springer, New York (2003)Google Scholar
  8. 8.
    Infanger, G.: Planning under Uncertainty. Boyd and Fraser, Danvers (1994)zbMATHGoogle Scholar
  9. 9.
    Martos, B.: The direct power of adjacet vertex programming methods. Man. Sc. 12, 241–252 (1965)MathSciNetGoogle Scholar
  10. 10.
    Sharma, I.C., Aggarwal, S.P.: Fractional programming in communication systems. Unternehmensforchung 14(2), 52–155 (1970)MathSciNetGoogle Scholar
  11. 11.
    Sinha, S.M.: A duality theorem on nonlinear programming. Man. Sc. 12, 385–390 (1966)Google Scholar
  12. 12.
    Swarup, K.: Linear fractional functionals programming. Oper. Res. 13, 1029–1036 (1965)zbMATHCrossRefGoogle Scholar

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© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of the South PacificSuvaFiji

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