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The Reverse Directional Distance Function

In: Advances in Efficiency and Productivity

Author

Listed:
  • Jesus T. Pastor

    (Miguel Hernandez University of Elche (UMH))

  • Juan Aparicio

    (Miguel Hernandez University of Elche (UMH))

  • Javier Alcaraz

    (Miguel Hernandez University of Elche (UMH))

  • Fernando Vidal

    (Miguel Hernandez University of Elche (UMH))

  • Diego Pastor

    (Physical and Sports Education Miguel Hernandez University of Elche (UMH))

Abstract

The aim of any Data EnvelopmentPastor, J.T. Analysis (DEA) inefficiency model is to calculate the efficient projection of each unit belonging to a certain finite sample. The reverse directional distance function (RDDF) is a new tool developed in this chapter that allows us to express any known DEA inefficiency model as a directional distance function (DDF). Hence, given a certain DEA inefficiency model, its RDDF is a specific DDF that truly reproduces the functioning of the considered DEA model. Automatically, all the interesting properties that apply to any DDF are directly transferable to the considered DEA model through its RDDF. Hence, the RDDF enlarges the set of properties exhibited by any DEA model. For instance, given any DEA inefficiency model, its economic inefficiency—in any of its three possible versions—, can be easily defined and decomposed as the sum of technical inefficiency and allocative inefficiency thanks to the RDDF. We further propose to transform any non-strong DDF into a strong DDF, i.e., into a DDF that projects all the units onto the strongly efficient frontier. This constitutes another indication of the transference capacity of the RDDF, because its strong version constitutes in itself a strong version of the original DEA model considered. We further propose to search for alternative projections so as to minimize profit inefficiency, and add an appendix showing how to search for multiple optimal solutions in additive-type models.

Suggested Citation

  • Jesus T. Pastor & Juan Aparicio & Javier Alcaraz & Fernando Vidal & Diego Pastor, 2016. "The Reverse Directional Distance Function," International Series in Operations Research & Management Science, in: Juan Aparicio & C. A. Knox Lovell & Jesus T. Pastor (ed.), Advances in Efficiency and Productivity, chapter 0, pages 15-57, Springer.
    • Handle: RePEc:spr:isochp:978-3-319-48461-7_2
    DOI: 10.1007/978-3-319-48461-7_2
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    Citations

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    Cited by:

    1. Sebastián Lozano & Narges Soltani & Akram Dehnokhalaji, 2020. "A compromise programming approach for target setting in DEA," Annals of Operations Research, Springer, vol. 288(1), pages 363-390, May.
    2. Sebastián Lozano & Narges Soltani, 2018. "DEA target setting using lexicographic and endogenous directional distance function approaches," Journal of Productivity Analysis, Springer, vol. 50(1), pages 55-70, October.
    3. Ester Gutiérrez & Sebastián Lozano, 2020. "Benchmarking Formula One auto racing circuits: a two stage DEA approach," Operational Research, Springer, vol. 20(4), pages 2059-2083, December.

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