Document Type : Research Paper


Department of Mathematics, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran.


The Cross-efficiency method in data envelopment analysis (DEA) has widely been used as a suitable utility for ranking decision-making units (DMUs). In this paper, for overcoming the issue of the existence of multiple optimal solutions in cross-efficiency evaluation, we use the neutral strategy to design a new secondary goal. Unlike the aggressive and benevolent formulations in cross-efficiency evaluation, the neutral cross-efficiency evaluation methods have been developed in a way that is only concerned with their own interests and is indifferent to other DMUs. The proposed secondary goal introduces a new cross-efficiency score by maximizing the sum of the output weights. The first model is then extended to a cross-weight evaluation, which seeks a common set of weights for all the DMUs. Finally, we give two numerical examples to illustrate the effectiveness of the proposed neutral models and the potential applications in ranking DMUs by comparing their solutions with those of alternative approaches.


Main Subjects

  • Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European journal of operational research2(6), 429-444.
  • Ucal Sari, I., & Ak, U. (2022). Machine efficiency measurement in industry 4.0 using fuzzy data envelopment analysis. Journal of fuzzy extension and applications3(2), 177-191.
  • Fallah, R., Kouchaki Tajani, M., Maranjory, M., & Alikhani, R. (2021). Comparison of banks and ranking of bank loans types on based of efficiency with dea in Iran. Big data and computing visions1(1), 36-51.
  • Muniz, R. D. F., Andriola, W. B., Muniz, S. M., & Thomaz, A. C. F. (2021). The use of data envelopment analysis (DEA) to estimate the educational efficiency of Brazilian schools. Journal of applied research on industrial engineering, 9(4), 374-383.
  • Ghaziyani, K., Ejlaly, B., & Bagheri, S. F. (2019). Evaluation of the efficiency by DEA a case study of hospital. International journal of research in industrial engineering8(3), 283-293.
  • Mirsadeghpour, M., Sanei, M., Tohidi, G., Banihashemi, S., & Modarresi, N. (In Press). Assets performance evaluation with the use of returns distribution characteristics. Journal of decisions and operations research. (In Persian).
  • Kayedppour, F., Sayadmanesh, S., Salmani, Y., & Sadeghi, Z. (2021). Measuring the efficiency and productivity of cement companies in Tehran Stock Exchange by data envelopment analysis and Malmquist productivity index in gray environment. Innovation management and operational strategies, 1(4), 363-382. (In Persian).
  • Li, F., Wu, H., Zhu, Q., Liang, L., & Kou, G. (2021). Data envelopment analysis cross efficiency evaluation with reciprocal behaviors. Annals of operations research302, 173-210.
  • Sexton, T. R., Silkman, R. H., & Hogan, A. J. (1986). Data envelopment analysis: critique and extensions. New directions for program evaluation1986(32), 73-105.
  • Doyle, J., & Green, R. (1994). Efficiency and cross-efficiency in DEA: derivations, meanings and uses. Journal of the operational research society45, 567-578.
  • Liang, L., Wu, J., Cook, W. D., & Zhu, J. (2008). The DEA game cross-efficiency model and its Nash equilibrium. Operations research56(5), 1278-1288.
  • Jahanshahloo, G. R., Hosseinzadeh Lotfi, F., Jafari, Y., & Maddahi, R. (2011). Selecting symmetric weights as a secondary goal in DEA cross-efficiency evaluation. Applied mathematical modelling35(1), 544-549.
  • Chen, L., Huang, Y., Li, M. J., & Wang, Y. M. (2020). Meta-frontier analysis using cross-efficiency method for performance evaluation. European journal of operational research280(1), 219-229.
  • Chen, L., & Wang, Y. M. (2020). DEA target setting approach within the cross efficiency framework. Omega96, 102072.
  • Chen, L., Wang, Y. M., & Huang, Y. (2020). Cross-efficiency aggregation method based on prospect consensus process. Annals of operations research288, 115-135.
  • Contreras, I., Lozano, S., & Hinojosa, M. A. (2021). A DEA cross-efficiency approach based on bargaining theory. Journal of the operational research society72(5), 1156-1167.
  • Wu, D., Wang, Y., Liu, Y., & Wu, J. (2021). DEA cross‐efficiency ranking method considering satisfaction and consensus degree. International transactions in operational research28(6), 3470-3492.
  • Wang, Y. M., & Chin, K. S. (2010). A neutral DEA model for cross-efficiency evaluation and its extension. Expert systems with applications37(5), 3666-3675.
  • Wang, Y. M., Chin, K. S., & Luo, Y. (2011). Cross-efficiency evaluation based on ideal and anti-ideal decision making units. Expert systems with applications38(8), 10312-10319.
  • Carrillo, M., & Jorge, J. M. (2018). An alternative neutral approach for cross-efficiency evaluation. Computers & industrial engineering120, 137-145.
  • Shi, H., Wang, Y., & Chen, L. (2019). Neutral cross-efficiency evaluation regarding an ideal frontier and anti-ideal frontier as evaluation criteria. Computers & industrial engineering132, 385-394.
  • Liu, H. H., Song, Y. Y., & Yang, G. L. (2019). Cross-efficiency evaluation in data envelopment analysis based on prospect theory. European journal of operational research273(1), 364-375.
  • Kao, C., & Liu, S. T. (2019). Cross efficiency measurement and decomposition in two basic network systems. Omega83, 70-79.
  • Örkcü, H. H., Özsoy, V. S., Örkcü, M., & Bal, H. (2019). A neutral cross efficiency approach for basic two stage production systems. Expert systems with applications125, 333-344.
  • Liu, P., Zhang, Y., & Xu, H. (2022). A neutral cross-efficiency measurement for general parallel production system. Expert systems with applications205, 117778.
  • Shi, H. L., Chen, S. Q., Chen, L., & Wang, Y. M. (2021). A neutral cross-efficiency evaluation method based on interval reference points in consideration of bounded rational behavior. European journal of operational research290(3), 1098-1110.
  • Wang, L., Song, X., & Song, X. (2021). Research on the measurement and spatial-temporal difference analysis of energy efficiency in China’s construction industry based on a game cross-efficiency model. Journal of cleaner production278, 123918.
  • Amin, G. R., & Hajjami, M. (2021). Improving DEA cross-efficiency optimization in portfolio selection. Expert systems with applications168, 114280.
  • Tofallis, C. (1997). Input efficiency profiling: an application to airlines. Computers & operations research24(3), 253-258.
  • Chiang, C. I., Hwang, M. J., & Liu, Y. H. (2011). Determining a common set of weights in a DEA problem using a separation vector. Mathematical and computer modelling54(9-10), 2464-2470.