An Interactive Approach for Multicriteria Decision Making Using a Tchebycheff Utility Function Approximation

Multicriteria decision making (MCDM) can provide an efficient mean for considering various and conflicting objectives to reveal the alternative that maximizes the decision maker's (DM) utility. In this paper, we propose a new interactive MCDM method for implicit alternatives to help a DM obtain a most preferred solution. We employ a Tchebycheff function to generate weights for objectives consistent with the DM's responses to pairwise comparisons between alternatives and present a mixed integer linear programming formulation to generate these weights. Thus, we approximate the DM's utility function by a Tchebycheff function and generate weights consistent with the DM's responses. We test our approach with different true utility functions on various sized multiple criteria linear programming problems. The computational results show that even with non-Tchebycheff true utility functions, our method can generate alternatives very close to the optimal solution with few questions. The comparison of our results with other methods reveals its advantages.