A Linear Fractional Max-Min Problem

W. D. Cook, M. J. L. Kirby and S. L. Mehndiratta
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W. D. Cook: York University, Toronto, Ontario
M. J. L. Kirby: Dalhousie University, Halifax, Nova Scotia
S. L. Mehndiratta: Dalhousie University, Halifax, Nova Scotia

Operations Research, 1975, vol. 23, issue 3, 511-521

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.

Date: 1975
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