A note on fractional interval programming

W. Bühler1
1Lehrstuhl für Unternehmensforschung, Technische Hochschule Aachen, Aachen

Tóm tắt

A linear fractional program of the form max (cx+r)/(dx+s) subject toa≤Ax≤b (FIP) is considered, whereA is am ×n matrix with rank(A)=m. By replacing (FIP) by a parametric linear program, in the first part of this paper the existence of an optimal solution of (FIP) is discussed. In the second part an algorithm is presented which is based upon an algorithm ofDinkelbach and takes into account the special structure of the constraints. The results are illustrated by an example.

Từ khóa


Tài liệu tham khảo

Ben-Israel, A., andA. Charnes: An Explicit Solution of a Special Class of Linear Programming Problems, in: Opns. Res.16, 1166–1175, 1968. Ben-Israel, A., A. Charnes, A. P. Hurter, andP. D. Robers: On the Explicit Solution of a Special Class of Linear Economic Models, in: Opns. Res.18, 462–470, 1970. Charnes, A., andW. W. Cooper: Programming with Linear Fractional Functionals, in: Nav. Res. Log. Quart.9, 181–186, 1962. Dinkelbach, W.: Die Maximierung eines Quotienten zweier linearer Funktionen unter linearen Nebenbedingungen, in: Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 1. Jg., 141–145, 1962. —: On Nonlinear Fractional Programming, in: Man. Science13, 492–498, 1967. Martos, B.: Hyperbolic Programming, in: Nav. Res. Log. Quart.11, 135–155, 1964. —: The Direct Power of Adjacent Vertex Programming Methods, in: Man. Science,12, 241–252, 1965. Swarup, K.: Upper Bound Problem in Linear Fractional Functionals Programming, in: Metrika15, 81–85, 1970.