An integrated super efficiency index based on entropy approach: the case of Chinese commercial banks

Document Type : Original Article

Authors

1 Faculty of Industrial Engineering and Management Science, Shahrood University of Technology

2 School of Economics and Statistics, Guangzhou University

Abstract
This paper proposes a novel integrated super efficiency method for ranking decision making units using data envelopment analysis. The integrated method is based on the effect of removing a unit from all possible aggregated units using Shannon entropy approach. In contrasted with the classical super efficiency method, we do not face infeasibility in our model. This is due to the fact that we do not alter the efficiency frontier in our model. An application of the proposed models for ranking Chinese commercial banks demonstrates the practical relevance and advanced future of our method.

Keywords

Subjects


[1] Adler, N., Friedman, L., & Sinuany-Stern, Z. (2002). Review of ranking methods in the data envelopment analysis context. European Journal of Operational Research, 140(2), 249-265.
[2] Aldamak, A., & Zolfaghari, S. (2017). Review of efficiency ranking methods in data envelopment analysis. Mea- surement, 106, 161-172.
[3] Andersen, P., & Petersen, N. C. (1993). A procedure for ranking efficient units in data envelopment analysis. Management Science, 39(10), 1261-1264.
[4] Ang, S., Chen, M., & Yang, F. (2018). Group cross-efficiency evaluation in data envelopment analysis: An application to Taiwan hotels. Computers & Industrial Engineering, 125, 190-199.
[5] Asmild, M., & Matthews, K. (2012). Multi-directional efficiency analysis of efficiency patterns in Chinese banks 19972008. European Journal of Operational Research, 219(2), 434-441.
[6] Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science, 30(9), 1078-1092.
[7] Bardhan, I., Bowlin, W. F., Cooper, W. W., & Sueyoshi, T. (1996). Models for efficiency dominance in data envelopment analysis. Journal of the Operations Research Society of Japan, 39, 322-332.
[8] Berger, A. N., & Humphrey, D. B. (1997). Efficiency of financial institutions: International survey and directions for future research. European Journal of Operational Research, 98(2), 175-212.
[9] Carrillo, M., & Jorge, J. M. (2016). A multiobjective DEA approach to ranking alternatives. Expert Systems with Applications, 50, 130-139.
[10] Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2(6), 429-444.
[11] Cook, W. D., & Kress, M. (1994). A multiple-criteria composite index model for quantitative and qualitative data. European Journal of Operational Research, 78(3), 367-379.
[12] Doyle, J., & Green, R. (1994). Efficiency and cross-efficiency in DEA: Derivations, meanings and uses. Journal of the Operational Research Society, 45(5), 567-578.
[13] Entani, T., Maeda, Y., & Tanaka, H. (2002). Dual models of interval DEA and its extension to interval data. European Journal of Operational Research, 136(1), 32-45.
[14] Friedman, L., & Sinuany-Stern, Z. (1997). Scaling units via the canonical correlation analysis and the data envelopment analysis. European Journal of Operational Research, 100(3), 629-637.
[15] Ghiyasi, M. (2016). A DEA production technology and its usage for incorporation of collaboration in efficiency analysis: an axiomatic approach. International Transactions in Operational Research.
[16] Golany, B. (1988). An interactive MOLP procedure for the extension of DEA to effectiveness analysis. Journal of the Operational Research Society, 39(8), 725-734.
[17] Halme, M., Joro, T., Korhonen, P., Salo, S., & Wallenius, J. (1999). A value efficiency approach to incorporating preference information in data envelopment analysis. Management Science, 45(1), 103-115.
[18] Halme, M., & Korhonen, P. J. (2015). Using value efficiency analysis to benchmark Nonhomogeneous units. International Journal of Information Technology & Decision Making, 14(4), 727-745.
[19] Hatefi, S., & Torabi, S. (2010). A common weight MCDADEA approach to construct composite indicators. Eco- logical Economics, 70(1), 114-120.
[20] Hosseinzadeh Lotfi, F., Jahanshahloo, G. R., Khodabakhshi, M., Rostamy-Malkhlifeh, M., Moghaddas, Z., & Vaez- Ghasemi, M. (2013). A review of ranking models in data envelopment analysis. Journal of Applied Mathematics, 2013.
[21] Jahanshahloo, G. R., Memariani, A., Lotfi, F. H., & Rezai, H. Z. (2005). A note on some of DEA models and finding efficiency and complete ranking using common set of weights. Applied Mathematics and Computation, 166(2), 265-281.
[22] Jenkins, L., & Anderson, M. (2003). A multivariate statistical approach to reducing the number of variables in data envelopment analysis. European Journal of Operational Research, 147(1), 51-61.
[23] Komarovska, A., Ustinovichius, L., Shevchenko, G., & Nazarko, L. (2015). Multicriteria evaluation of commercial industrial zone development. International Journal of Strategic Property Management, 19(1), 84-95.
[24] Lu, T., & Liu, S.-T. (2016). Ranking DMUs by Comparing DEA Cross-Efficiency Intervals Using Entropy Measures. Entropy, 18(12), 452.
[25] Ma, X., Xu, X., Wang, Z., Zhao, X., Lee, H., & Truskolaski, T. (2024). Technological innovation, industrial structure upgrading and mining energy efficiency: An analysis based on the super-efficient EBM model. Resources Policy, 98, 105339.
[26] Oukil, A. (2018). Ranking via composite weighting schemes under a DEA cross-evaluation framework. Computers & Industrial Engineering, 117, 217-224.
[27] Qi, X.-G., & Guo, B. (2014). Determining common weights in data envelopment analysis with Shannons entropy. Entropy, 16(12), 6394-6414.
[28] Ramón, N., Ruiz, J. L., & Sirvent, I. (2012). Common sets of weights as summaries of DEA profiles of weights: With an application to the ranking of professional tennis players. Expert Systems with Applications, 39(5), 4882-4889.
[29] Seiford, L. M., & Zhu, J. (1999). Infeasibility of super-efficiency data envelopment analysis models. Infor, 37(2), 174-187.
[30] Sexton, T. R., Silkman, R. H., & Hogan, A. J. (1986). Data envelopment analysis: Critique and extensions. New Directions for Program Evaluation, 1986(32), 73-105.
[31] Sinuany-Stern, Z., & Friedman, L. (1998). DEA and the discriminant analysis of ratios for ranking units. European Journal of Operational Research, 111(3), 470-478.
[32] Sinuany-Stern, Z., Mehrez, A., & Barboy, A. (1994). Academic departments efficiency via DEA. Computers & Operations Research, 21(5), 543-556.
[33] Soleimani-Damaneh, M., & Zarepisheh, M. (2009). Shannons entropy for combining the efficiency results of different DEA models: Method and application. Expert Systems with Applications, 36(3), 5146-5150.
[34] Sun, J., Wu, J., Wang, Y., Li, L., & Wang, Y. (n.d.). Crossefficiency evaluation method based on the conservative point of view. Expert Systems, e12336.
[35] Taleb, M., Khalid, R., Attallah, M., Ramli, R., & Mohd Nawawi, M. K. (2023). Evaluating efficiency and ranking of suppliers using non-radial super-efficiency data envelopment analysis with uncontrollable factors. International Journal of Computer Mathematics: Computer Systems Theory, 8(2), 108-127.
[36] Thanassoulis, E., & Dyson, R. (1992). Estimating preferred target input-output levels using data envelopment analysis. European Journal of Operational Research, 56(1), 80-97.
[37] Torgersen, A. M., Førsund, F. R., & Kittelsen, S. A. (1996). Slack-adjusted efficiency measures and ranking of efficient units. Journal of Productivity Analysis, 7(4), 379-398.
[38] Wang, Y.-M., Luo, Y., & Hua, Z. (2007). Aggregating preference rankings using OWA operator weights. Information Sciences, 177(16), 3356-3363.
[39] Wu, J., Sun, J., & Liang, L. (2012). DEA cross-efficiency aggregation method based upon Shannon entropy. International Journal of Production Research, 50(23), 6726-6736.
[40] Wu, J., Sun, J., Liang, L., & Zha, Y. (2011). Determination of weights for ultimate cross efficiency using Shannon entropy. Expert Systems with Applications, 38(5), 5162-5165.
[41] Yamada, Y. T., M., & M., S. (1994). An inefficiency measurement method for management-systems. Journal of the Operations Research Society of Japan, 3, 158-168.
[42] Zhao, X., Ma, X., Shang, Y., Yang, Z., & Shahzad, U. (2022). Green economic growth and its inherent driving factors in Chinese cities: Based on the Metafrontier-global-SBM super-efficiency DEA model. Gondwana Research, 106, 315-328.
[43] Zhong, K., Wang, Y., Pei, J., Tang, S., & Han, Z. (2021). Super efficiency SBM-DEA and neural network for performance evaluation. Information Processing & Management, 58(6), 102728.
Volume 6, Issue 2
Spring 2025
Pages 64-71

  • Receive Date 10 December 2024
  • Revise Date 04 March 2025
  • Accept Date 04 March 2025