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

  • Ke Wang
  • Yujiao Xian
  • Chia-Yen Lee
  • Yi-Ming Wei
  • Zhimin Huang
DEA in Data Analytics


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.


Data envelopment analysis (DEA) Least distance Endogenous mechanism Cost efficiency Profit efficiency Marginal profit maximization 



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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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Ke Wang
    • 1
    • 2
    • 3
  • Yujiao Xian
    • 1
  • Chia-Yen Lee
    • 4
  • Yi-Ming Wei
    • 1
    • 2
    • 3
  • Zhimin Huang
    • 1
    • 5
  1. 1.Center for Energy and Environmental Policy Research & School of Management and EconomicsBeijing Institute of TechnologyBeijingChina
  2. 2.Collaborative Innovation Center of Electric Vehicles in BeijingBeijingChina
  3. 3.Sustainable Development Research Institute for Economy and Society of BeijingBeijingChina
  4. 4.Institute of Manufacturing Information and SystemsNational Cheng Kung UniversityTainanTaiwan
  5. 5.Robert B. Willumstad School of BusinessAdelphi UniversityGarden CityUSA

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