SETS OF EFFICIENT SOLUTIONS FOR DISCRETE BICRITERIA OPTIMIZATION

PROBLEMS ^{∗}

P. Fernández^{1} ^{†}, J. Fernández^{1}, B. Pelegrín^{1} and T. B. Boffey^{2}

1Dept. of Statistics and Operations Research, University of Murcia, Spain

2Dept. of Mathematical Sciences, University of Liverpool, U.K.

Abstract

This paper deals with a general bicriterion model with a finite set of feasible solutions. First, we define various types of efficient solution sets for discrete multiobjective problems, which are especially useful for the decision maker, e.g. efficient, inferior and superior efficient, extreme efficient, and inferior and superior extreme efficient solution sets. Second, for every one of the different types of efficient solution sets, we propose a method to obtain the whole solution set. The techniques presented do not allow preferences to be incorporated into the solution process. Finally, some bicriterion problems are mentioned as particular cases of the general model.

Keywords: bicriterion optimization models, efficient solutions.

∗This research has been partially supported by the Fundación Séneca under grant PB/11/FS/97 †To whom all correspondence should be addressed.