Advertisement

Zeitschrift für Operations Research

, Volume 16, Issue 3, pp 91–100 | Cite as

On duality in linear fractional functionals programming

  • I. C. Sharma
  • K. Swarup
Article

Summary

The paper formulates a dual program for a given linear fractional functionals program (L.F.F.P.) and proves the duality theorem and its converse for the same. Special feature of the paper is that both the primal and the dual programs are L. F. F. Ps. and can easily be solved by the existing standard techniques.

Keywords

Standard Technique Duality Theorem Functional Program Dual Program Fractional Functional 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Zusammenfassung

Für ein lineares Optimierungsproblem, dessen Zielfunktion als Quotient zweier linearer Funktionen gegeben ist (LP-Problem mit gebrochener Zielfunktion), wird ein duales Problem formuliert und das Dualitätstheorem bewiesen. Es wird gezeigt, daß sowohl das primale als auch das duale Problem lineare Probleme mit gebrochener Zielfunktion sind und leicht mit den bekannten Standardtechniken gelöst werden können.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bector, C. R.: Duality in Fractional and Indefinite Programming. ZAMM,48, Heft 6, 418–420, 1968.Google Scholar
  2. Charnes, A., andW. W. Cooper: Programming with Linear Fractional Functional. Nav. Res. Log. Quart.,9, 181–186, 1962.Google Scholar
  3. Dinkelbach, W.: Die Maximierung eines Quotienten zweier linearer Funktionen unter linearen Nebenbedingungen. Z. Wahrscheinlichkeitstheorie,1, 141–145, 1962.CrossRefGoogle Scholar
  4. Dorn, W. S.: Linear fractional programming. I.B.M. Research Report, 1962.Google Scholar
  5. —: A duality theorem for convex programs. I. B.M. J. Res. Development,4, 407–413, 1960.Google Scholar
  6. Hadley, G.: Linear Programming. Addison Wesly Series in Industrial Management, Reading Mass, 1962.Google Scholar
  7. Martos, B.: Hyperbolic Programming. Nav. Res. Log. Quart.,11, 135–155, 1964.Google Scholar
  8. —: The Direct Power of Adjacent Vertex Programming Methods, Manag. Sc.,12, No. 3, 241–252, 1965.Google Scholar
  9. Swarup, K.: Linear Fractional Functionals Programming. Operations Res.,13, No. 6, 1029–1036, 1965.Google Scholar
  10. —: Duality in Fractional Programming. Unternehmensforschung,12, Heft 2, 106–112, 1968.Google Scholar
  11. —: Some Aspects of Duality in Fractional Programming. ZAMM, 47, 204, 1967.Google Scholar
  12. Wolfe, P.: A duality Theorem for Non-Linear Programming. Quart. App. Math.,19, 239–244, 1961.Google Scholar

Copyright information

© Physica-Verlag 1972

Authors and Affiliations

  • I. C. Sharma
    • 1
  • K. Swarup
    • 2
  1. 1.R & D OrganisationMinistry of DefenceNew DelhiIndia
  2. 2.Faculty of MathematicsDelhi UniversityDelhi-7India

Personalised recommendations