An interactive MCDM weight space reduction method utilizing a Tchebycheff utility function

Employing a Tchebycheff utility function to locally approximate the underlying utility function, the authors develop an interactive method to solve multiple-objective linear programming problems involving a single decision maker. They utilize selected and consistent weights in an augmented Tchebycheff linear programming formulation to obtain nondominated alternatives. Based on pairwise comparisons between alternatives, the authors generate constraints on the weights used to combine the decision maker’s objectives. The constraints, formed to be consistent with a Tchebycheff function, lead to multiple disjoint convex regions in weight space. An algorithm is presented, and its performance is compared to the Zionts-Walenius method for various true underlying utility functions.