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On selecting directions for directional distance functions in a non-parametric framework: a review

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Abstract

Directional distance function (DDF) has been a commonly used technique for estimating efficiency and productivity over the past two decades, and the directional vector is usually predetermined in the applications of DDF. The most critical issue of using DDF remains that how to appropriately project the inefficient decision-making unit onto the production frontier along with a justified direction. This paper provides a comprehensive literature review on the techniques for selecting directional vector of the directional distance function. It begins with a brief introduction of the existing methods around the inclusion of the exogenous direction techniques and the endogenous direction techniques. The former commonly includes arbitrary direction and conditional direction techniques, while the latter involves the techniques for seeking theoretically optimized directions (i.e., direction towards the closest benchmark or indicating the largest efficiency improvement potential) and market-oriented directions (i.e., directions towards cost minimization, profit maximization, or marginal profit maximization benchmarks). The main advantages and disadvantages of these techniques are summarized, and the limitations inherent in the exogenous direction-selecting techniques are discussed. It also analytically argues the mechanism of each endogenous direction technique. The literature review is end up with a numerical example of efficiency estimation for power plants, in which most of the reviewed directions for DDF are demonstrated and their evaluation performance are compared.

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Notes

  1. The hyperbolic efficiency measure (Färe et al. 1989) is excluded in this study since the model does not provide a linear direction vector which can be used in DDF and shows a nonlinear optimization problem.

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Acknowledgements

We gratefully acknowledge the financial support from the National Natural Science Foundation of China (Grant Nos. 71471018, 71521002, and 71642004), the Joint Development Program of Beijing Municipal Commission of Education, the Social Science Foundation of Beijing (Grant No. 16JDGLB013), the National Key R&D Program (Grant No. 2016YFA0602603), and the Ministry of Science and Technology of Taiwan (MOST103-2221-E-006-122-MY3).

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Authors and Affiliations

  1. Center for Energy and Environmental Policy Research & School of Management and Economics, Beijing Institute of Technology, Beijing, China

    Ke Wang, Yujiao Xian, Yi-Ming Wei & Zhimin Huang

  2. Collaborative Innovation Center of Electric Vehicles in Beijing, Beijing, China

    Ke Wang & Yi-Ming Wei

  3. Sustainable Development Research Institute for Economy and Society of Beijing, Beijing, China

    Ke Wang & Yi-Ming Wei

  4. Institute of Manufacturing Information and Systems, National Cheng Kung University, Tainan, Taiwan

    Chia-Yen Lee

  5. Robert B. Willumstad School of Business, Adelphi University, Garden City, NY, USA

    Zhimin Huang

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  1. Ke Wang
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Wang, K., Xian, Y., Lee, CY. et al. On selecting directions for directional distance functions in a non-parametric framework: a review. Ann Oper Res 278, 43–76 (2019). https://doi.org/10.1007/s10479-017-2423-5

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