Associated with the objective set Y of a linear k-objective minimization problem is the efficiency equivalent polyhedron &Ytilde; = Y + R(k)(+). Since &Ytilde; has the same efficient structure as Y and since every extreme point of &Ytilde; is efficient, this polyhedron provides a promising avenue for the analysis of the given multiple objective linear program (MOLP). However, in order to fully explore this avenue, a representation of &Ytilde; as a system of linear inequalities is needed. In this paper an algorithm is given to construct a matrix H and a vector g such that &Ytilde; has the representation Hy ≥ g, and it is shown that no inequality in this representation is redundant. The input data for the algorithm are a finite set of points of Y containing the efficient extreme points and a finite set of recession directions for Y containing the directions associated with unbounded efficient edges. These data, which can be obtained using standard MOLP software packages, are used to form a polar polyhedron whose extreme points are precisely what is needed to define H and g.
