A Dual Approach to Nonconvex Frontier Models

This paper extends the links between the non-parametric data envelopment analysis (DEA) models for efficiency analysis, duality theory and multi-criteria decision making models for the linear and non-linear case. By drawing on the properties of a partial Lagrangean relaxation, a correspondence is shown between the CCR, BCC and free disposable hull (FDH) models in DEA and the MCDM model. One of the implications is a characterization that verifies the sufficiency of the weighted scalarizing function, even for the non-convex case FDH. A linearization of FDH is presented along with dual interpretations. Thus, an input/output-oriented model is shown to be equivalent to a maximization of the weighted input/output, subject to production space feasibility. The discussion extends to the recent developments: the free replicability 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.