An algorithm based on facial decomposition for finding the efficient set in multiple objective linear programming

We propose a method for finding the efficient set of a multiple objective linear program based on the well-known facial decomposition of the efficient set. The method incorporates a simple linear programming test that identifies efficient faces while employing a top--down search strategy which avoids enumeration of efficient extreme points and locates the maximally efficient faces of the feasible region. We suggest that discrete representations of the efficient faces could be obtained and presented to the Decision Maker. Results of computational experiments are reported.