A dual approach to nonconvex frontier models

This paper extends the links between the non-parametric data envelopment an alysis (DEA) models for efficiency analysis, duality theory and multi-crite ria decision making models for the linear and non-linear case. By drawing o n the properties of a partial Lagrangean relaxation, a correspondence is sh own between the CCR, BCC and free disposable hull (FDH) models in DEA and t he MCDM model. One of the implications is a characterization that verifies the sufficiency of the weighted scalarizing function, even for the non-conv ex case FDH. A linearization of FDH is presented along with dual interpreta tions. Thus, an input/output-oriented model is shown to be equivalent to a maximization of the weighted input/output, subject to production space feas ibility. The discussion extends to the recent developments: the free replic ability hull (FRH), the new elementary replicability hull (ERH) and the non -convex models by Petersen (1990). FRH is shown to be a true mixed integer program, whereas the latter can be characterized as the CCR and BCC models.