A Dual Approach to Nonconvex Frontier Models

Per Agrell () and Jørgen Tind

Journal of Productivity Analysis, 2001, vol. 16, issue 2, 129-147

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. Copyright Kluwer Academic Publishers 2001

Keywords: DEA; MCDM; dualization; FDM (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (27)

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DOI: 10.1023/A:1011679226885

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