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A Linear Fractional Max-Min Problem

Author

Listed:
  • W. D. Cook

    (York University, Toronto, Ontario)

  • M. J. L. Kirby

    (Dalhousie University, Halifax, Nova Scotia)

  • S. L. Mehndiratta

    (Dalhousie University, Halifax, Nova Scotia)

Abstract

This paper is concerned with a linear fractional problem of the form: max X min Y F ( X , Y ) = ( cX + dY + α)/( fX + gY + β), subject to \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland,xspace}\usepackage{amsmath,amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$$AX + BY \leq b; \quad X, Y \geq 0.$$\end{document} This problem represents a generalization of a problem considered in the literature in which F ( X , Y ) is assumed to be linear. A number of results for the linear case are extended; and, in particular, it is shown that this fractional max-min problem is equivalent to a quasi-convex programming problem whose optimal solution lies at a vertex of the feasible region. Using these results, we develop an algorithm for solving this problem. The paper concludes with a numerical example.

Suggested Citation

  • W. D. Cook & M. J. L. Kirby & S. L. Mehndiratta, 1975. "A Linear Fractional Max-Min Problem," Operations Research, INFORMS, vol. 23(3), pages 511-521, June.
    • Handle: RePEc:inm:oropre:v:23:y:1975:i:3:p:511-521
    DOI: 10.1287/opre.23.3.511
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