A Dual Approach to Nonconvex Frontier Models |
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Authors: | Agrell Per J Tind Jørgen |
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Institution: | (1) Department of Economics, Royal Agricultural University, DK-1958 Frederiksberg C, Denmark;(2) Department of Statistics and Operations Research, University of Copenhagen, DK-2100 Copenhagen, Denmark |
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Abstract: | 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. |
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Keywords: | DEA MCDM dualization FDM |
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