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On the DEA total weight flexibility and the aggregation in cross-efficiency evaluations

Author

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  • Ruiz, José L.
  • Sirvent, Inmaculada

Abstract

This paper discusses the DEA total weight flexibility in the context of the cross-efficiency evaluation. The DMUs in DEA are often assessed with unrealistic weighting schemes in their attempt to achieve the best ratings in their self-evaluation. We claim here that in a peer-appraisal like the cross-efficiency evaluation the cross-efficiencies provided by such weights cannot play the same role as those obtained with more reasonable weights. To address this issue, we propose to calculate the cross-efficiency scores by means of a weighted average of cross-efficiencies, instead of with the usual arithmetic mean, so the aggregation weights reflect the disequilibrium in the profiles of DEA weights that are used. Thus, the cross-efficiencies provided by profiles with large differences in their weights, especially those obtained with zero weights, would be attached lower aggregation weights (less importance) than those provided by more balanced profiles of weights.

Suggested Citation

  • Ruiz, José L. & Sirvent, Inmaculada, 2012. "On the DEA total weight flexibility and the aggregation in cross-efficiency evaluations," European Journal of Operational Research, Elsevier, vol. 223(3), pages 732-738.
  • Handle: RePEc:eee:ejores:v:223:y:2012:i:3:p:732-738
    DOI: 10.1016/j.ejor.2012.06.011
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    References listed on IDEAS

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    1. Cooper, William W. & Ruiz, Jose L. & Sirvent, Inmaculada, 2007. "Choosing weights from alternative optimal solutions of dual multiplier models in DEA," European Journal of Operational Research, Elsevier, vol. 180(1), pages 443-458, July.
    2. Ramón, Nuria & Ruiz, José L. & Sirvent, Inmaculada, 2010. "A multiplier bound approach to assess relative efficiency in DEA without slacks," European Journal of Operational Research, Elsevier, vol. 203(1), pages 261-269, May.
    3. 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.
    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. 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.
    6. Timothy Anderson & Keith Hollingsworth & Lane Inman, 2002. "The Fixed Weighting Nature of A Cross-Evaluation Model," Journal of Productivity Analysis, Springer, vol. 17(3), pages 249-255, May.
    7. 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.
    8. 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.
    9. 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.
    10. R. Allen & A. Athanassopoulos & R.G. Dyson & E. Thanassoulis, 1997. "Weights restrictions and value judgements in Data Envelopment Analysis: Evolution, development and future directions," Annals of Operations Research, Springer, vol. 73(0), pages 13-34, October.
    11. 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.
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    Cited by:

    1. repec:spr:annopr:v:255:y:2017:i:1:d:10.1007_s10479-015-1881-x is not listed on IDEAS
    2. Galagedera, Don U.A., 2014. "Modeling risk concerns and returns preferences in performance appraisal: An application to global equity markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 33(C), pages 400-416.
    3. 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.
    4. Ruiz, José L., 2013. "Cross-efficiency evaluation with directional distance functions," European Journal of Operational Research, Elsevier, vol. 228(1), pages 181-189.

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