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An aggressive game cross-efficiency evaluation in data envelopment analysis

Author

Listed:
  • Wenli Liu

    (Fuzhou University
    Fuzhou University)

  • Ying-Ming Wang

    (Fuzhou University)

  • Shulong Lv

    (Fuzhou University
    Fuzhou University)

Abstract

Cross-efficiency evaluation is an effective method for ranking decision making units (DMUs) in data envelopment analysis, which is performed with peer-evaluation and self-evaluation. From different points of view, various cross-efficiency evaluations have been proposed with different secondary goals. Yet they usually lead to different average cross-efficiencies and different rankings. In this paper, we develop a concept of the aggressive game cross-efficiency, and propose an aggressive secondary model to minimize the cross-efficiencies of other DMUs under the constraints that the aggressive game cross-efficiency of the evaluated DMU is guaranteed. To achieve the aggressive game cross-efficiency, we develop an iterative algorithm. Mathematically, it is proved that all conventional average cross-efficiencies are sure to converge to the same aggressive game cross-efficiency by the iterative algorithm. Finally, numerical examples are presented to show the effectiveness of our approach in evaluating and ranking DMUs.

Suggested Citation

  • Wenli Liu & Ying-Ming Wang & Shulong Lv, 2017. "An aggressive game cross-efficiency evaluation in data envelopment analysis," Annals of Operations Research, Springer, vol. 259(1), pages 241-258, December.
    • Handle: RePEc:spr:annopr:v:259:y:2017:i:1:d:10.1007_s10479-017-2524-1
    DOI: 10.1007/s10479-017-2524-1
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    1. Wang, Ying-Ming & Chin, Kwai-Sang, 2010. "Some alternative models for DEA cross-efficiency evaluation," International Journal of Production Economics, Elsevier, vol. 128(1), pages 332-338, November.
    2. 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.
    3. Seyed Rakhshan & Ali Kamyad & Sohrab Effati, 2015. "Ranking decision-making units by using combination of analytical hierarchical process method and Tchebycheff model in data envelopment analysis," Annals of Operations Research, Springer, vol. 226(1), pages 505-525, March.
    4. Ramón, Nuria & Ruiz, José L. & Sirvent, Inmaculada, 2010. "On the choice of weights profiles in cross-efficiency evaluations," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1564-1572, December.
    5. Lim, Sungmook & Oh, Kwang Wuk & Zhu, Joe, 2014. "Use of DEA cross-efficiency evaluation in portfolio selection: An application to Korean stock market," European Journal of Operational Research, Elsevier, vol. 236(1), pages 361-368.
    6. Y M Wang & K S Chin & J B Yang, 2007. "Measuring the performances of decision-making units using geometric average efficiency," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(7), pages 929-937, July.
    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. Jie Wu & Liang Liang & Dexiang Wu & Feng Yang, 2008. "Olympics ranking and benchmarking based on cross efficiency evaluation method and cluster analysis: the case of Sydney 2000," International Journal of Enterprise Network Management, Inderscience Enterprises Ltd, vol. 2(4), pages 377-392.
    9. Green, Rodney H. & Doyle, John R. & Cook, Wade D., 1996. "Preference voting and project ranking using DEA and cross-evaluation," European Journal of Operational Research, Elsevier, vol. 90(3), pages 461-472, May.
    10. Joe Zhu, 2014. "DEA Cross Efficiency," International Series in Operations Research & Management Science, in: Quantitative Models for Performance Evaluation and Benchmarking, edition 3, chapter 4, pages 61-92, Springer.
    11. Entani, Tomoe & Maeda, Yutaka & Tanaka, Hideo, 2002. "Dual models of interval DEA and its extension to interval data," European Journal of Operational Research, Elsevier, vol. 136(1), pages 32-45, January.
    12. Ruiz, José L., 2013. "Cross-efficiency evaluation with directional distance functions," European Journal of Operational Research, Elsevier, vol. 228(1), pages 181-189.
    13. Chen, Tser-yieth, 2002. "An assessment of technical efficiency and cross-efficiency in Taiwan's electricity distribution sector," European Journal of Operational Research, Elsevier, vol. 137(2), pages 421-433, March.
    14. Sinuany-Stern, Zilla & Friedman, Lea, 1998. "DEA and the discriminant analysis of ratios for ranking units," European Journal of Operational Research, Elsevier, vol. 111(3), pages 470-478, December.
    15. Shang, Jen & Sueyoshi, Toshiyuki, 1995. "A unified framework for the selection of a Flexible Manufacturing System," European Journal of Operational Research, Elsevier, vol. 85(2), pages 297-315, September.
    16. Muhittin Oral & Ossama Kettani & Pascal Lang, 1991. "A Methodology for Collective Evaluation and Selection of Industrial R&D Projects," Management Science, INFORMS, vol. 37(7), pages 871-885, July.
    17. Xiyang Lei & Yongjun Li & Qiwei Xie & Liang Liang, 2015. "Measuring Olympics achievements based on a parallel DEA approach," Annals of Operations Research, Springer, vol. 226(1), pages 379-396, March.
    18. Liang, Liang & Wu, Jie & Cook, Wade D. & Zhu, Joe, 2008. "Alternative secondary goals in DEA cross-efficiency evaluation," International Journal of Production Economics, Elsevier, vol. 113(2), pages 1025-1030, June.
    19. Jahanshahloo, Gholam Reza & Junior, Helcio Vieira & Lotfi, Farhad Hosseinzadeh & Akbarian, Darush, 2007. "A new DEA ranking system based on changing the reference set," European Journal of Operational Research, Elsevier, vol. 181(1), pages 331-337, August.
    20. Ali Emrouznejad, 2014. "Advances in data envelopment analysis," Annals of Operations Research, Springer, vol. 214(1), pages 1-4, March.
    21. C Kao & H-T Hung, 2005. "Data envelopment analysis with common weights: the compromise solution approach," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(10), pages 1196-1203, October.
    22. Youchao Tan & Yang Zhang & Roohollah Khodaverdi, 2017. "Service performance evaluation using data envelopment analysis and balance scorecard approach: an application to automotive industry," Annals of Operations Research, Springer, vol. 248(1), pages 449-470, January.
    23. D K Despotis, 2002. "Improving the discriminating power of DEA: focus on globally efficient units," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(3), pages 314-323, March.
    24. Jie Wu & Junfei Chu & Qingyuan Zhu & Pengzhen Yin & Liang Liang, 2016. "DEA cross-efficiency evaluation based on satisfaction degree: an application to technology selection," International Journal of Production Research, Taylor & Francis Journals, vol. 54(20), pages 5990-6007, October.
    25. Jie Wu & Junfei Chu & Qingyuan Zhu & Yongjun Li & Liang Liang, 2016. "Determining common weights in data envelopment analysis based on the satisfaction degree," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(12), pages 1446-1458, December.
    26. Wu, Jie & Liang, Liang & Chen, Yao, 2009. "DEA game cross-efficiency approach to Olympic rankings," Omega, Elsevier, vol. 37(4), pages 909-918, August.
    27. 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.
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