Independent, convergent, and divergent decision behaviour for interactive multiple objectives linear programming

An interactive paired comparison approach for multiple objective linear programming (MOLP) problems is developed where the Decision Maker's preferential behaviour is presented by a utility function. The preferential behaviour can be independent, convergent, or divergent; which are mathematically presented by additive, quasi-concave, or quasi-convex utility functions respectively. The approach to find the best alternative consists of four phases: I. An additive utility function. II. A quasi-concave utility function. III. A quasi-convex utility function. IV. A feasible goal utility function. In the first three phases a paired comparison of alternatives are used and in Phase IV a feasible goal method is developed that finds the closest feasible efficient point for a given goal by the decision maker. This method also identifies resources required to make a given goal feasible. The approach can be extended to solve multiple objective integer/nonlinear optimization problems. Some experiments and examples are provided.