A new interactive algorithm for multi-objective linear programming using maximally changeable dominance cone

Abstract

The purpose of this research is to develop a computer applicable interactive methodology for the resolution of multi-objective linear decision problems within a decision makers (DMs) capability to supply necessary information for problem solution. Enlarging the (Pareto) dominance cone is subject to the condition that the set of all efficient solutions does not change. This leads to the recently developed concept of the Maximally changeable dominance cone which is proved to be strictly negative polar cone generated by the positive outer normal vectors of all maximally efficient facets. In this study, it is shown that by enlarging the dominance cone, the number of efficient solutions in the objective space becomes smaller. Therefore, our method reduces interactively the subset of efficient solutions in the objective space by enlarging the (Pareto) dominance cone step by step based on the DMs preference information until only a few efficient solutions remain. From these, then, the DM can select his/her most preferred one. In the beginning of the procedure, the concept of the intervals of pairwise tradeoffs between objectives, called the Marginal Rate of Substitution (MRS), is applied as a candidate for screening the efficient solutions which are less preferable. Furthermore, appropriate questions founded on the notion of the MRS are posed to the DM in order to eliminate the less preferable solutions from consideration in the solution process, which results in enlargement of the dominance cone. A numerical example is provided to illustrate the procedure described. © 1993.