Constructing the set of efficient objective values in multiple objective linear programs

In earlier work the authors developed an algebraic description of the polyhedron Y=C[X], where C is a k×n matrix and X={x∈ℝⁿ: Ax∈b∈. This algebraic description was then used to determine the Pareto-efficient objective values of the multiple objective linear program: maximize Cx, x∈X. In this paper, this approach is modified to obtain a more efficient procedure. In addition, a resulting single-objective nonparametric linear program in ℝ^k’+¹ is developed whose set of optimal basic solution corresponds to the set of efficient extreme points of Y.