IDEAS home Printed from https://ideas.repec.org/a/spr/operea/v25y2025i1d10.1007_s12351-025-00901-9.html
   My bibliography  Save this article

A super-efficiency model based on the directional distance function under a new direction

Author

Listed:
  • Weiwei Zhu

    (Nanjing University of Posts and Telecommunications
    Jiangsu University of Science and Technology)

  • Zhaowen Bai

    (Nanjing University of Posts and Telecommunications)

  • Yu Yu

    (Nanjing Audit University)

Abstract

In order to solve the problem that the super-efficiency model based on directional distance function (DDF) is unable to handle negative data and infeasible under the assumption of variation in returns to scale (VRS), by choosing a suitable direction is an useful method. However, the newly chosen direction may lead to the emergence of weakly efficient projection point, which reduces the efficiency identification ability of the original model. In this paper, new direction is provided for the super-efficiency DDF model to overcome the problem of reducing the identification ability of the model. The new direction can provide strong efficient projection point for the inefficient decision making units (DMUs). The contributions of this paper are mainly as follows: (1) We find and explain the problem that the super-efficiency DDF model may have the issue of not being able to distinguish the efficiency of inefficient DMUs efficiently under some directions. (2) A new direction is provided under which the super-efficiency DDF model has a stronger ability to distinguish between the efficiency. (3) The new direction can also handle negative data while being able to ensure that the model is always feasible.

Suggested Citation

  • Weiwei Zhu & Zhaowen Bai & Yu Yu, 2025. "A super-efficiency model based on the directional distance function under a new direction," Operational Research, Springer, vol. 25(1), pages 1-19, March.
    • Handle: RePEc:spr:operea:v:25:y:2025:i:1:d:10.1007_s12351-025-00901-9
    DOI: 10.1007/s12351-025-00901-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s12351-025-00901-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s12351-025-00901-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Per Andersen & Niels Christian Petersen, 1993. "A Procedure for Ranking Efficient Units in Data Envelopment Analysis," Management Science, INFORMS, vol. 39(10), pages 1261-1264, October.
    2. Lee, Hsuan-Shih & Chu, Ching-Wu & Zhu, Joe, 2011. "Super-efficiency DEA in the presence of infeasibility," European Journal of Operational Research, Elsevier, vol. 212(1), pages 141-147, July.
    3. Chen, Yao & Du, Juan & Huo, Jiazhen, 2013. "Super-efficiency based on a modified directional distance function," Omega, Elsevier, vol. 41(3), pages 621-625.
    4. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    5. Ruiyue Lin & Zhiping Chen, 2017. "A directional distance based super-efficiency DEA model handling negative data," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(11), pages 1312-1322, November.
    6. Cheng, Gang & Zervopoulos, Panagiotis & Qian, Zhenhua, 2013. "A variant of radial measure capable of dealing with negative inputs and outputs in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 225(1), pages 100-105.
    7. M C A Silva Portela & E Thanassoulis & G Simpson, 2004. "Negative data in DEA: a directional distance approach applied to bank branches," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(10), pages 1111-1121, October.
    8. Emrouznejad, Ali & Anouze, Abdel Latef & Thanassoulis, Emmanuel, 2010. "A semi-oriented radial measure for measuring the efficiency of decision making units with negative data, using DEA," European Journal of Operational Research, Elsevier, vol. 200(1), pages 297-304, January.
    9. Lin, Ruiyue & Liu, Yue, 2019. "Super-efficiency based on the directional distance function in the presence of negative data," Omega, Elsevier, vol. 85(C), pages 26-34.
    10. Chen, Yao & Liang, Liang, 2011. "Super-efficiency DEA in the presence of infeasibility: One model approach," European Journal of Operational Research, Elsevier, vol. 213(1), pages 359-360, August.
    11. W D Cook & L Liang & Y Zha & J Zhu, 2009. "A modified super-efficiency DEA model for infeasibility," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(2), pages 276-281, February.
    12. Ruiyue Lin & Zhiping Chen, 2015. "Super-efficiency measurement under variable return to scale: an approach based on a new directional distance function," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(9), pages 1506-1510, September.
    13. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
    14. Guo-Ya Gan & Hsuan-Shih Lee, 2021. "Resolving the infeasibility of the super-efficiency DEA based on DDF," Annals of Operations Research, Springer, vol. 307(1), pages 139-152, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lin, Ruiyue & Liu, Yue, 2019. "Super-efficiency based on the directional distance function in the presence of negative data," Omega, Elsevier, vol. 85(C), pages 26-34.
    2. Ruiyue Lin & Zhiping Chen, 2017. "A directional distance based super-efficiency DEA model handling negative data," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(11), pages 1312-1322, November.
    3. Lin, Ruiyue & Li, Zongxin, 2020. "Directional distance based diversification super-efficiency DEA models for mutual funds," Omega, Elsevier, vol. 97(C).
    4. Guo-Ya Gan & Hsuan-Shih Lee, 2021. "Resolving the infeasibility of the super-efficiency DEA based on DDF," Annals of Operations Research, Springer, vol. 307(1), pages 139-152, December.
    5. Tavana, Madjid & Izadikhah, Mohammad & Toloo, Mehdi & Roostaee, Razieh, 2021. "A new non-radial directional distance model for data envelopment analysis problems with negative and flexible measures," Omega, Elsevier, vol. 102(C).
    6. Ghasemi, M.-R. & Ignatius, Joshua & Emrouznejad, Ali, 2014. "A bi-objective weighted model for improving the discrimination power in MCDEA," European Journal of Operational Research, Elsevier, vol. 233(3), pages 640-650.
    7. Rezaeiani, M.J. & Foroughi, A.A., 2018. "Ranking efficient decision making units in data envelopment analysis based on reference frontier share," European Journal of Operational Research, Elsevier, vol. 264(2), pages 665-674.
    8. Lin, Shuguang & Shi, Hai-Liu & Wang, Ying-Ming, 2022. "An integrated slacks-based super-efficiency measure in the presence of nonpositive data," Omega, Elsevier, vol. 111(C).
    9. Kao, Chiang, 2020. "Measuring efficiency in a general production possibility set allowing for negative data," European Journal of Operational Research, Elsevier, vol. 282(3), pages 980-988.
    10. Lee, Hsuan-Shih, 2022. "Integrating SBM model and Super-SBM model: a one-model approach," Omega, Elsevier, vol. 113(C).
    11. Arabmaldar, Aliasghar & Sahoo, Biresh K. & Ghiyasi, Mojtaba, 2023. "A generalized robust data envelopment analysis model based on directional distance function," European Journal of Operational Research, Elsevier, vol. 311(2), pages 617-632.
    12. Fang, Hsin-Hsiung & Lee, Hsuan-Shih & Hwang, Shiuh-Nan & Chung, Cheng-Chi, 2013. "A slacks-based measure of super-efficiency in data envelopment analysis: An alternative approach," Omega, Elsevier, vol. 41(4), pages 731-734.
    13. Zohreh Sadeghi & Reza Farzipoor Saen & Mahdi Moradzadehfard, 2022. "RETRACTED ARTICLE: Developing a network data envelopment analysis model for appraising sustainable supply chains: a sustainability accounting approach," Operations Management Research, Springer, vol. 15(3), pages 809-824, December.
    14. Atwood, Joseph & Shaik, Saleem, 2020. "Theory and statistical properties of Quantile Data Envelopment Analysis," European Journal of Operational Research, Elsevier, vol. 286(2), pages 649-661.
    15. Zervopoulos, Panagiotis & Emrouznejad, Ali & Sklavos, Sokratis, 2019. "A Bayesian approach for correcting bias of data envelopment analysis estimators," MPRA Paper 91886, University Library of Munich, Germany.
    16. Cheng, Gang & Zervopoulos, Panagiotis, 2012. "A proxy approach to dealing with the infeasibility problem in super-efficiency data envelopment analysis," MPRA Paper 42064, University Library of Munich, Germany.
    17. Lin, Ruiyue & Liu, Qian, 2021. "Multiplier dynamic data envelopment analysis based on directional distance function: An application to mutual funds," European Journal of Operational Research, Elsevier, vol. 293(3), pages 1043-1057.
    18. Ghasemi, Mohammad Reza & Ignatius, Joshua & Rezaee, Babak, 2019. "Improving discriminating power in data envelopment models based on deviation variables framework," European Journal of Operational Research, Elsevier, vol. 278(2), pages 442-447.
    19. Guo-Ya Gan & Hsuan-Shih Lee, 2019. "An alternative MILP-DEA model to choose efficient unit without explicit inputs," Annals of Operations Research, Springer, vol. 278(1), pages 379-391, July.
    20. Lee, Hsuan-Shih & Zhu, Joe, 2012. "Super-efficiency infeasibility and zero data in DEA," European Journal of Operational Research, Elsevier, vol. 216(2), pages 429-433.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:operea:v:25:y:2025:i:1:d:10.1007_s12351-025-00901-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.