AN EXACT INTERACTIVE METHOD FOR EXPLORING THE EFFICIENT FACETS OF MULTIPLE OBJECTIVE LINEAR-PROGRAMMING PROBLEMS WITH QUASI-CONCAVE UTILITY-FUNCTIONS

Many real-world problems can be formulated as multiple-objective linear programming (MOLP) problems. In the search for the best compromise solution for conflicting and noncommensurate objectives, a quasiconcave preference structure (utility function) is used that is more flexible and general than pseudoconcave, concave, and linear utility functions. Since the complete assessment of such a utility function is very difficult or impossible, an interactive method is developed in which, with a minimum of simple questions to the decision-maker (DM), the best compromise solution can be obtained. The DM responds to either paired comparison or simple trade-off questions. The method also uses linear approximations of the nonlinear utility function to improve convergence rate. Several tests are given to obtain preferred alternatives by generating and using partial information on local approximations of the nonlinear utility function. The method obtains the most preferred alternative by moving directly on efficient facets of MOLP. A procedure is provided for identifying efficient tradeoffs on the efficient facet so that only efficient alternatives are generated. For the first time, onvergence with a limited number of questions is proven for quasiconcave and pseudoconcave utility functions.