(An) interactive algorithm for solving multiobjective linear programming using dominance cone

Abstract

The purpose of this study is to develop a computer applicable methodology for solving multiobjective linear programming problem by using dominance cone with the aid of decision maker. The dominance cone has been proved to be negative polar cone generated by the positive outer normal vectors of the efficient facets associated with the decision maker``s responses. In this study, it is shown that by enlarging the dominance cone number of efficient facets in the objective space becomes smaller. Therefore, our proposed method reduces iteratively the subset of efficient facets in the objective space by enlarging the dominance cone step by step until only a few efficient points remain. From these then the decision maker can select his/her best preferred one. A numerical example is provided to illustrate the procedure described.