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Abstract
Associated with the objective set Y of a linear k-objective minimization problem is the efficiency equivalent polyhedron Y ≔ Y + R + k . Since Y has the same efficient structure as Y and since every extreme point of Y 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 Y 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 Y 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.
Published Version
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