The Enumeration of the Set of All Efficient Solutions for a Linear Multiple Objective Program

Abstract

This paper presents an algorithm for the enumeration of the set of all efficient solutions for a linear multiple objective program. The procedure first finds whether an efficient solution exists for a given linear multiple objective program and then determines an initial efficient basic solution. In a second step the set of all efficient basic solutions and of all efficient extreme rays is established. Finally, the set of all efficient solutions is constructed as a union of a minimal number of convex sets of efficient solutions. The procedure developed in this paper will be illustrated by a numerical example.