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Fractional Programming with Zero-One Variables

  • Conference paper
Extremal Methods and Systems Analysis

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 174))

Abstract

Charnes and Cooper (1962) introduced a simple linear programming formulation of the problem of maximizing the ratio of two linear functions of variables subject to linear constraints. This paper shows that the formulation can be applied to problems including zero-one decision variables without requiring any new optimization algorithm when using a code that allows Special Ordered Sets of Type One as defined by Beale and Tomlin (1970).

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References

  1. Beale, Evelyn M.L., John A. Tomlin: Special facilities in a general mathematical programming system for nonconvex problems using ordered sets of variables in Proceedings of the Fifth International Conference on Operational Research. Ed. Lawrence J. London: Tavistock Publications, 1970, 447–454.

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  2. Charnes, Abraham, William W. COOPER: Programming with Linear Fractional Functionals. Naval Research Logistics Quarterly 9 (1962), 181–186.

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  3. Granot, Daniel, Freda Granot: On Solving Fractional (0,1) Programs by Implicit Enumeration. INFOR 14 (1976), 241–249.

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  4. Granot, Daniel, Freda Granot: On Integer and Mixed Integer Fractional Programming Problems. Annals of Discrete Mathematics 1 (1977), 221–231.

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  5. Williams, Hilary P.: Experiments in the formulation of integer programming problems. Mathematical Programming Study 2 (1974), 180–197.

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Authors
  1. E. M. L. Beale
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Editor information

Editors and Affiliations

  1. Department of Operations Research Institute for Management Science and Engineering, The Washington University, 20052, Washington, DC, USA

    Anthony V. Fiacco

  2. Department of Mathematics, Carnegie-Mellon University, 15213, Pittsburgh, PA, USA

    Kenneth O. Kortanek

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© 1980 Springer-Verlag Berlin Heidelberg

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Beale, E.M.L. (1980). Fractional Programming with Zero-One Variables. In: Fiacco, A.V., Kortanek, K.O. (eds) Extremal Methods and Systems Analysis. Lecture Notes in Economics and Mathematical Systems, vol 174. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46414-0_21

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  • DOI: https://doi.org/10.1007/978-3-642-46414-0_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09730-3

  • Online ISBN: 978-3-642-46414-0

  • eBook Packages: Springer Book Archive

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