An Alternative Approach to Rank Efficient DMUs in DEA via Cross-Efficiency Evaluation, Gini Coefficient, and Bonferroni Mean

  • Zahra Behdani
  • Majid DarehmirakiEmail author


In this paper, we focus on a critical problem in data envelopment analysis (DEA) and propose a simple resolution for it. The major problem of the DEA is the existence of several efficient decision-making units (DMUs). To deal with this issue, we introduce a method that involves cross-efficiency evaluation, Gini coefficient, and Bonferroni mean. First, a cross-efficiency matrix is developed. Then, mixing the Gini coefficient and Bonferroni mean, a Gini–Bonferroni (GB) index is proposed for ranking efficient DMUs, where the DMUs with bigger GB are ranked higher. The proposed method broke the tie between efficient DMUs. Finally, a numerical example and real application of this method are presented in the ranking of research and development (R&D) investment companies in the pharmaceutical and biotechnology industries.


Data envelopment analysis Efficiency Gini coefficient Bonferroni mean Cross-efficiency evaluation Ranking Efficient units 

Mathematics Subject Classification

90B50 97K80 



The authors thank the organizers of ICO2018, 4–5th October 2018, Hard Rock Hotel, Pattaya, Thailand, for the opportunity to presents their research results in this paper.


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Copyright information

© Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsBehbahan Khatam Alanbia University of TechnologyBehbahanIran

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