Finding Efficient Solutions for Bilevel Linear Multi-Objective Programming Problems

We consider bilevel linear multi-objective programming problems (BLMPP) in which the decision maker has multiple objective functions conflicting with each other at each level. We show how to construct two artificial multi-objective programming problems such that any point that is efficient for both problems is an efficient solution of the BLMPP. A necessary and sufficient condition which is applicable for the obtained result is provided. Then, based on these results, the algorithm is presented. Finally, we give an example to show the efficiency of the algorithm.