Max-Min Programming with Linear Fractional Functions; Algorithms and Examples

Abstract

Consider the following problem:

$$\max imize\,z(x)=\underset{i=1\ldots r}{\mathop{\min }}\,\frac{{{c}^{i}}x+{{\alpha }_{i}}}{{{d}^{i}}+{{\beta }_{i}}}\,subject\,to\,x\varepsilon s=\{x|Ax\le b,x\ge 0\}$$

(1)

where cⁱ, dⁱ are row vectors, with dⁱ x + β_i > 0 for x ε S. (1) is a linear fractional max-min programming (LFMMP) problem. In this paper we will present two algorithms for the solution of the problem and give some initial computational experience.