Duality Based Characterizations of Efficient Facets

Abstract

Most practical applications of multicriteria decision making can be formulated in terms of efficient points determined by preference cones with polyhedral closure. Using linear approximations and duality from mathematical programming, we characterize a family of supporting hyperplanes that define the efficient facets of a set of alternatives with respect to such preference cones. We show that a subset of these hyperplanes generate maximal efficient facets. These characterizations permit us to devise a new algorithm for generating all maximal efficient facets of multicriteria optimization problems with polyhedral structure.