An Algorithm for Solving the Linear Goal Programming Problem by Solving its Dual

Abstract

Goal programming, and in particular lexicographic goal programming (i.e. goal programming within a so-called ‘pre-emptive priority’ structure or having non-Archimedean weights), has become one of the most widely used of the approaches for multi-objective mathematical programming. While also applicable to non-linear or integer models, most of the literature has considered the lexicographic linear goal-programming model and its solution via primal simplex-based methods. However, in many cases, enhanced efficiency (and significant additional flexibility) may be gained via an investigation of the dual of this problem. In this paper we consider an algorithm for solving such a dual and also indicate how it may be implemented on conventional (i.e. single objective) simplex software.