On a bicriterion max-min fractional problem. (English) Zbl 0753.90064

Ţigan, Ş.; Stancu-Minasian, I. M.

Math., Rev. Anal. Numér. Théor. Approximation, Anal. Numér. Théor. Approximation 20, No. 1-2, 117-125 (1991).

We consider a max-min bicriterion fractional problem with separate linear constraints. We prove that this problem can be transformed into a bicriterion fractional maximization problem. For this last type of nonlinear program, A. R. Warburton [Oper. Res. 33, 74-84 (1985; Zbl 0569.90088)] described a finite procedure which consists in solving a one-parameter linear program and a series of one-dimensional maximizations. Another approach to the general multiobjective linear- fractional programming was presented by R. Weber [“Pseudomonotonic multiobjective programming”, Discussion Pap. B 8203, Inst. Oper. Res., Univ. of Saarland, Saarbrücken/Ger., 1982)]. He considered an interactive procedure for the pseudomonotonic multiobjective programming, to obtain an efficient solution which satisfies some decision maker’s preferences.
Our algorithm for the bicriterion max-min fractional problem consists in applying Warburton’s procedure to solve a certain bicriterion fractional maximization program.

MSC:

90C32

Fractional programming

Keywords:

max-min bicriterion fractional problem; separate linear constraints; bicriterion max-min fractional problem

Citations:

Zbl 0569.90088