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 ε{lunate} 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 ε{lunate} X. In this paper, this approach is modified to obtain a more efficient procedure. In addition, a resulting single-objective nonparametric linear program in Rk+1 is developed whose set of optimal basic solutions corresponds to the set of efficient extreme points of Y. © 1990.