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A Dual Approach to Nonconvex Frontier Models

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  • Per Agrell
  • Jørgen Tind

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

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  • Per Agrell & Jørgen Tind, 2001. "A Dual Approach to Nonconvex Frontier Models," Journal of Productivity Analysis, Springer, vol. 16(2), pages 129-147, September.
    • Handle: RePEc:kap:jproda:v:16:y:2001:i:2:p:129-147
    DOI: 10.1023/A:1011679226885
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    References listed on IDEAS

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