Goal programming duality revisited: Formulation of a set of variant duals

Abstract

The formulation of the duals of the original goal programming variants took place in the decades following its introduction, principally for computational purposes. However the development of more recent Goal Programming variants has not been matched by the formulation and analysis of their associated duals. This paper furthers the topic of goal programming duality by formulating the duals of a progressive sequence of up to the most recent Goal Programming models: Weighted, Chebyshev, Extended and Extended Network Goal Programming models. It interprets the results and shows the insights that the duals can provide, principally by providing an understanding of the interactions between the multiple objectives in each case. The paper concludes with a comparison of the results and shows how the sequence of duals mirrors the sequence of the associated primals.