IDEAS home Printed from https://ideas.repec.org/a/eee/jomega/v95y2020ics0305048319307728.html
   My bibliography  Save this article

A slacks-based measure model for calculating cross efficiency in data envelopment analysis

Author

Listed:
  • Kao, Chiang
  • Liu, Shiang-Tai

Abstract

Cross efficiency is a concept for solving the problem of incomparability among the efficiencies of a set of decision making units (DMUs) calculated from different weights in data envelopment analysis, and is helpful for ranking. Conventional cross efficiency is a radial measure, and the radial measure has some weaknesses. First, it is not able to provide appropriate efficiency scores for weakly efficient DMUs. Second, the efficiencies measured from the input and output sides under variable returns to scale are different which may cause difficulties in subsequent analyses. Third, negative values may appear when the efficiency is measured from the input side. To solve these problems, this paper proposes a slacks-based measure to calculate efficiency. The basic idea is the same as that of the radial measure using the frontier corresponding to a DMU to measure the efficiency of all DMUs, except that the efficiency measure is slacks-based instead of radial. Due to the nature of the slacks-based efficiency measure, the problems caused by weak efficiency and difference in input and output radial measures do not exist. More importantly, negative efficiencies are not produced. The proposed method is applied to a real case involving the selection of the most efficient robot to use for production. The results help identify the top-ranked robot.

Suggested Citation

  • Kao, Chiang & Liu, Shiang-Tai, 2020. "A slacks-based measure model for calculating cross efficiency in data envelopment analysis," Omega, Elsevier, vol. 95(C).
    • Handle: RePEc:eee:jomega:v:95:y:2020:i:c:s0305048319307728
    DOI: 10.1016/j.omega.2020.102192
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0305048319307728
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.omega.2020.102192?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. Nuria Ramón & José L Ruiz & Inmaculada Sirvent, 2014. "Dominance relations and ranking of units by using interval number ordering with cross-efficiency intervals," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(9), pages 1336-1343, September.
    2. Yang, Feng & Ang, Sheng & Xia, Qiong & Yang, Chenchen, 2012. "Ranking DMUs by using interval DEA cross efficiency matrix with acceptability analysis," European Journal of Operational Research, Elsevier, vol. 223(2), pages 483-488.
    3. Song, Malin & An, Qingxian & Zhang, Wei & Wang, Zeya & Wu, Jie, 2012. "Environmental efficiency evaluation based on data envelopment analysis: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 16(7), pages 4465-4469.
    4. 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.
    5. Wang, Ying-Ming & Chin, Kwai-Sang, 2011. "The use of OWA operator weights for cross-efficiency aggregation," Omega, Elsevier, vol. 39(5), pages 493-503, October.
    6. Tone, Kaoru & Tsutsui, Miki, 2009. "Network DEA: A slacks-based measure approach," European Journal of Operational Research, Elsevier, vol. 197(1), pages 243-252, August.
    7. 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.
    8. Y-M Wang & K-S Chin & S Wang, 2012. "DEA models for minimizing weight disparity in cross-efficiency evaluation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 63(8), pages 1079-1088, August.
    9. Sungmook Lim & Joe Zhu, 2015. "DEA Cross Efficiency Under Variable Returns to Scale," International Series in Operations Research & Management Science, in: Joe Zhu (ed.), Data Envelopment Analysis, edition 127, chapter 3, pages 45-66, Springer.
    10. Ramón, Nuria & Ruiz, José L. & Sirvent, Inmaculada, 2011. "Reducing differences between profiles of weights: A "peer-restricted" cross-efficiency evaluation," Omega, Elsevier, vol. 39(6), pages 634-641, December.
    11. Yu, Gang & Wei, Quanling & Brockett, Patrick & Zhou, Li, 1996. "Construction of all DEA efficient surfaces of the production possibility set under the Generalized Data Envelopment Analysis Model," European Journal of Operational Research, Elsevier, vol. 95(3), pages 491-510, December.
    12. Sungmook Lim & Joe Zhu, 2015. "DEA cross-efficiency evaluation under variable returns to scale," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(3), pages 476-487, March.
    13. Soares de Mello, João Carlos C.B. & Angulo Meza, Lidia & da Silveira, Juliana Quintanilha & Gomes, Eliane Gonçalves, 2013. "About negative efficiencies in Cross Evaluation BCC input oriented models," European Journal of Operational Research, Elsevier, vol. 229(3), pages 732-737.
    14. Mostafa Davtalab-Olyaie, 2019. "A secondary goal in DEA cross-efficiency evaluation: A “one home run is much better than two doubles” criterion," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 70(5), pages 807-816, May.
    15. Wade D. Cook & Joe Zhu, 2015. "DEA Cross Efficiency," International Series in Operations Research & Management Science, in: Joe Zhu (ed.), Data Envelopment Analysis, edition 127, chapter 2, pages 23-43, Springer.
    16. Jahanshahloo, G.R. & Shirzadi, A. & Mirdehghan, S.M., 2009. "Finding strong defining hyperplanes of PPS using multiplier form," European Journal of Operational Research, Elsevier, vol. 194(3), pages 933-938, May.
    17. Alcaraz, Javier & Ramón, Nuria & Ruiz, José L. & Sirvent, Inmaculada, 2013. "Ranking ranges in cross-efficiency evaluations," European Journal of Operational Research, Elsevier, vol. 226(3), pages 516-521.
    18. Shiang-Tai Liu, 2018. "A DEA ranking method based on cross-efficiency intervals and signal-to-noise ratio," Annals of Operations Research, Springer, vol. 261(1), pages 207-232, February.
    19. A. Charnes & W. W. Cooper, 1962. "Programming with linear fractional functionals," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 9(3‐4), pages 181-186, September.
    20. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
    21. Ole Olesen & N. Petersen, 2003. "Identification and Use of Efficient Faces and Facets in DEA," Journal of Productivity Analysis, Springer, vol. 20(3), pages 323-360, November.
    22. Tone, Kaoru, 2001. "A slacks-based measure of efficiency in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 130(3), pages 498-509, May.
    23. Mostafa Davtalab Olyaie & Israfil Roshdi & Gholamreza Jahanshahloo & Masoud Asgharian, 2014. "Characterizing and finding full dimensional efficient facets in DEA: a variable returns to scale specification," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(9), pages 1453-1464, September.
    24. Wu, Jie & Liang, Liang & Chen, Yao, 2009. "DEA game cross-efficiency approach to Olympic rankings," Omega, Elsevier, vol. 37(4), pages 909-918, August.
    25. Liang Liang & Jie Wu & Wade D. Cook & Joe Zhu, 2008. "The DEA Game Cross-Efficiency Model and Its Nash Equilibrium," Operations Research, INFORMS, vol. 56(5), pages 1278-1288, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hao Pan & Guo-liang Yang & Xiao-lei Chen & Yuan-yu Lou & Teng Wang & Zhong-cheng Guan, 2024. "Regret cross-efficiency evaluation using attitudinal entropy approach," Palgrave Communications, Palgrave Macmillan, vol. 11(1), pages 1-17, December.
    2. Chen, Xiaolei & Guan, Zhongcheng & Yang, Guoliang & Pan, Hao & Xiong, Xi, 2024. "Evaluation of technology transfer performance for Chinese universities based on a dual-game cross-efficiency model," Socio-Economic Planning Sciences, Elsevier, vol. 94(C).
    3. Xing, Peixue & Wang, Yanan & Ye, Tao & Sun, Ying & Li, Qiao & Li, Xiaoyan & Li, Meng & Chen, Wei, 2024. "Carbon emission efficiency of 284 cities in China based on machine learning approach: Driving factors and regional heterogeneity," Energy Economics, Elsevier, vol. 129(C).
    4. Davtalab-Olyaie, Mostafa & Asgharian, Masoud, 2021. "On Pareto-optimality in the cross-efficiency evaluation," European Journal of Operational Research, Elsevier, vol. 288(1), pages 247-257.
    5. Borrás, Fernando & Ruiz, José L. & Sirvent, Inmaculada, 2023. "Peer evaluation through cross-efficiency based on reference sets," Omega, Elsevier, vol. 114(C).
    6. Zhu, Qingyuan & Aparicio, Juan & Li, Feng & Wu, Jie & Kou, Gang, 2022. "Determining closest targets on the extended facet production possibility set in data envelopment analysis: Modeling and computational aspects," European Journal of Operational Research, Elsevier, vol. 296(3), pages 927-939.
    7. Ebrahimi, Bohlool & Dhamotharan, Lalitha & Ghasemi, Mohammad Reza & Charles, Vincent, 2022. "A cross-inefficiency approach based on the deviation variables framework," Omega, Elsevier, vol. 111(C).
    8. Khoso, Ali Raza & Yusof, Aminah Md & Chen, Zhen-Song & Skibniewski, Mirosław J. & Chin, Kwai-Sang & Khahro, Shabir Hussain & Sohu, Samiullah, 2022. "Comprehensive analysis of state-of-the-art contractor selection models in construction environment-A critical review and future call," Socio-Economic Planning Sciences, Elsevier, vol. 79(C).
    9. Ali Homayoni & Reza Fallahnejad & Farhad Hosseinzadeh Lotfi, 2022. "Cross Malmquist Productivity Index in Data Envelopment Analysis," 4OR, Springer, vol. 20(4), pages 567-602, December.
    10. Aparicio, Juan & Zofío, José L., 2021. "Economic cross-efficiency," Omega, Elsevier, vol. 100(C).
      • Aparicio, J. & Zofío, J.L., 2019. "Economic Cross-Efficiency," ERIM Report Series Research in Management ERS-2019-001-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    11. Sweksha Srivastava & Abha Aggarwal & Pooja Bansal, 2024. "Efficiency Evaluation of Assets and Optimal Portfolio Generation by Cross Efficiency and Cumulative Prospect Theory," Computational Economics, Springer;Society for Computational Economics, vol. 63(1), pages 129-158, January.
    12. Feng Li & Han Wu & Qingyuan Zhu & Liang Liang & Gang Kou, 2021. "Data envelopment analysis cross efficiency evaluation with reciprocal behaviors," Annals of Operations Research, Springer, vol. 302(1), pages 173-210, July.

    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. Liu, John S. & Lu, Louis Y.Y. & Lu, Wen-Min, 2016. "Research fronts in data envelopment analysis," Omega, Elsevier, vol. 58(C), pages 33-45.
    2. Feng Li & Han Wu & Qingyuan Zhu & Liang Liang & Gang Kou, 2021. "Data envelopment analysis cross efficiency evaluation with reciprocal behaviors," Annals of Operations Research, Springer, vol. 302(1), pages 173-210, July.
    3. Ebrahimi, Bohlool & Dhamotharan, Lalitha & Ghasemi, Mohammad Reza & Charles, Vincent, 2022. "A cross-inefficiency approach based on the deviation variables framework," Omega, Elsevier, vol. 111(C).
    4. Andreas Dellnitz & Elmar Reucher & Andreas Kleine, 2021. "Efficiency evaluation in data envelopment analysis using strong defining hyperplanes," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(2), pages 441-465, June.
    5. Davtalab-Olyaie, Mostafa & Asgharian, Masoud, 2021. "On Pareto-optimality in the cross-efficiency evaluation," European Journal of Operational Research, Elsevier, vol. 288(1), pages 247-257.
    6. Alcaraz, Javier & Aparicio, Juan & Monge, Juan Fco & Ramón, Nuria, 2022. "Weight profiles in cross-efficiency evaluation based on hypervolume maximization," Socio-Economic Planning Sciences, Elsevier, vol. 82(PB).
    7. Juan Aparicio & José L. Zofío, 2020. "New Definitions of Economic Cross-efficiency," International Series in Operations Research & Management Science, in: Juan Aparicio & C. A. Knox Lovell & Jesus T. Pastor & Joe Zhu (ed.), Advances in Efficiency and Productivity II, pages 11-32, Springer.
    8. Shiang-Tai Liu & Yueh-Chiang Lee, 2021. "Fuzzy measures for fuzzy cross efficiency in data envelopment analysis," Annals of Operations Research, Springer, vol. 300(2), pages 369-398, May.
    9. Cui, Yuan & Pan, Hao & Huang, Yi-Di & Yang, Guo-liang, 2024. "How can sociological theories provide legitimacy to eco-efficiency evaluations? Embark on a journey toward understanding," Socio-Economic Planning Sciences, Elsevier, vol. 93(C).
    10. Mostafa Davtalab-Olyaie & Hadis Mahmudi-Baram & Masoud Asgharian, 2023. "Measuring individual efficiency and unit influence in centrally managed systems," Annals of Operations Research, Springer, vol. 321(1), pages 139-164, February.
    11. Amineh Ghazi & Farhad Hosseinzadeh Lotfi & Masoud Sanei, 2020. "Hybrid efficiency measurement and target setting based on identifying defining hyperplanes of the PPS with negative data," Operational Research, Springer, vol. 20(2), pages 1055-1092, June.
    12. Oukil, Amar, 2020. "Exploiting value system multiplicity and preference voting for robust ranking," Omega, Elsevier, vol. 94(C).
    13. Hao Pan & Guo-liang Yang & Xiao-lei Chen & Yuan-yu Lou & Teng Wang & Zhong-cheng Guan, 2024. "Regret cross-efficiency evaluation using attitudinal entropy approach," Palgrave Communications, Palgrave Macmillan, vol. 11(1), pages 1-17, December.
    14. Ganji, S.S. & Dehghani, Alireza & Ajirlu, Shahrouz Fathi, 2024. "Evaluation of intercity road passenger transportation using a novel double-frontier game-regret-cross-efficiency," Socio-Economic Planning Sciences, Elsevier, vol. 93(C).
    15. Aparicio, Juan & Zofío, José L., 2021. "Economic cross-efficiency," Omega, Elsevier, vol. 100(C).
      • Aparicio, J. & Zofío, J.L., 2019. "Economic Cross-Efficiency," ERIM Report Series Research in Management ERS-2019-001-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    16. Ramón, Nuria & Ruiz, José L. & Sirvent, Inmaculada, 2020. "Cross-benchmarking for performance evaluation: Looking across best practices of different peer groups using DEA," Omega, Elsevier, vol. 92(C).
    17. Ruiz, José L., 2013. "Cross-efficiency evaluation with directional distance functions," European Journal of Operational Research, Elsevier, vol. 228(1), pages 181-189.
    18. Ji, Xiang & Li, Guo & Wang, Zhaohua, 2017. "Impact of emission regulation policies on Chinese power firms’ reusable environmental investments and sustainable operations," Energy Policy, Elsevier, vol. 108(C), pages 163-177.
    19. Xiang Ji & Jiasen Sun & Qunwei Wang & Qianqian Yuan, 2019. "Revealing Energy Over-Consumption and Pollutant Over-Emission Behind GDP: A New Multi-criteria Sustainable Measure," Computational Economics, Springer;Society for Computational Economics, vol. 54(4), pages 1391-1421, December.
    20. Shiang-Tai Liu, 2018. "A DEA ranking method based on cross-efficiency intervals and signal-to-noise ratio," Annals of Operations Research, Springer, vol. 261(1), pages 207-232, February.

    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:eee:jomega:v:95:y:2020:i:c:s0305048319307728. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/375/description#description .

    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.