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Enumeration algorithms for FDH directional distance functions under different returns to scale assumptions

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Abstract

Computing directional distance functions for a free disposal hull (FDH) technology in general requires solving nonlinear mixed integer programs. Cherchye et al. (J Product Anal 15(3):201–215, 2001) provide an enumeration algorithm for the FDH directional distance function in case of a variable returns to scale technology. In this contribution, we provide fast enumeration algorithms for the FDH directional distance functions under constant, nonincreasing, and nondecreasing returns to scale assumptions. Consequently, enumeration algorithms are now available for all commonly used returns to scale assumptions.

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Fig. 1
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Notes

  1. One often uses the moniker Data Envelopment Analysis (DEA) when imposing convexity on technology.

  2. These same authors also innovate methodologically by adding lower and upper bound restrictions to scaling in these extended FDH models.

  3. Note that the directional distance function is more general than the graph-oriented efficiency measure mentioned above. First, the direction vector can take any values. Second, while the directional distance function is dual to the profit function, a graph-oriented (or hyperbolic) efficiency measure is only dual to the return to the dollar function which measures profitability (see Färe et al. 2002).

  4. Sometimes the motivation to maintain convexity is just analytical convenience (see, e.g., Hackman 2008, p. 2). This is an argument that can hardly be taken seriously.

  5. Other measures (e.g., plant capacity utilization measures) can easily be derived from the choices mentioned here.

  6. Empirical data sets of this size are rarely publicly available [e.g., in the Journal of Applied Econometrics Data Archive (http://qed.econ.queensu.ca/jae/)] for the purpose of our illustration.

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Authors and Affiliations

  1. CNRS-LEM (UMR 9221), IESEG School of Management, 3 rue de la Digue, 59000, Lille, France

    Kristiaan Kerstens

  2. Research Unit MEES, KU Leuven, Warmoesberg 26, 1000, Brussel, Belgium

    Ignace Van de Woestyne

Authors
  1. Kristiaan Kerstens
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  2. Ignace Van de Woestyne
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Correspondence to Kristiaan Kerstens.

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We acknowledge helpful comments of three most constructive referees. The usual disclaimer applies.

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Kerstens, K., Van de Woestyne, I. Enumeration algorithms for FDH directional distance functions under different returns to scale assumptions. Ann Oper Res 271, 1067–1078 (2018). https://doi.org/10.1007/s10479-018-2791-5

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