Fuzzy Cross Efficiency Measurement for Two-Stage Network DEA
محورهای موضوعی : فصلنامه ریاضیAbdol Hossein Tajik Yabr 1 , S. Esmaeil Najafi 2 , Zohreh Moghaddas 3 , Parisa Shahnazari Shahrezaei 4
1 - Department of Industrial Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran
2 - Department of Industrial Engineering, Science and Research Branch of the Islamic Azad University, Tehran, Iran.
3 - Department of Industrial Engineering, Qazvin Branch, Qazvin, Iran.
4 - Department of Industrial Engineering, Islamic Azad University, Branch of Firoozkouh, Firoozkouh, Iran.
کلید واژه: data envelopment analysis , Network Data Envelopment Analysis , Fuzzy Data Envelopment Analysis , fuzzy cross efficiency,
چکیده مقاله :
The data envelopment analysis (DEA), as a nonparametric method in operational research, is used to measure the efficiency of a set of homogeneous decision-making units (DMU) with the help of linear programming. Up to now, this method has been extended to be used in various fields. For example, cross-efficiency evaluation, as a ranking technique, has been developed to address the challenges of traditional models. Moreover, the Fuzzy Data Envelopment Analysis (FDEA) and the Network Data Envelopment Analysis (NDEA) have been proposed to be used in terms of imprecise data and systems with internal processes, respectively. The existing models do not work when a decision maker tries to measure the efficiency under all these conditions, and thus there is a need for a unified model that considers all these conditions. In the present study, we present several models to measure the fuzzy cross efficiency of a general two-stage system. The aim of this study is to use the proposed models in the banking industry. In this regard, a case study is conducted to rank the branches of one of Iranian banks. Finally, we compare the results derived using the proposed models.
The data envelopment analysis (DEA), as a nonparametric method in operational research, is used to measure the efficiency of a set of homogeneous decision-making units (DMU) with the help of linear programming. Up to now, this method has been extended to be used in various fields. For example, cross-efficiency evaluation, as a ranking technique, has been developed to address the challenges of traditional models. Moreover, the Fuzzy Data Envelopment Analysis (FDEA) and the Network Data Envelopment Analysis (NDEA) have been proposed to be used in terms of imprecise data and systems with internal processes, respectively. The existing models do not work when a decision maker tries to measure the efficiency under all these conditions, and thus there is a need for a unified model that considers all these conditions. In the present study, we present several models to measure the fuzzy cross efficiency of a general two-stage system. The aim of this study is to use the proposed models in the banking industry. In this regard, a case study is conducted to rank the branches of one of Iranian banks. Finally, we compare the results derived using the proposed models.
[1] A. Charnes, W. W. Cooper, and E. Rhodes, “Measuring the efficiency of decision making units,” European Journal of Operational Research, vol. 2, no. 6, pp. 429–444, 1978.
[2] A. H. Tajik Yabr, S. E. Najafi, Z. Moghaddas, and P. Shahnazari Shahrezaei, "Interval Cross Efficiency Measurement for General Two‐Stage Systems, " Mathematical Problems in Engineering, 5431358, 2022.
[3] M. J. Farrell, “/e measurement of productive efficiency,” Journal of the Royal Statistical Society: Series A, vol. 120, no. 3, pp. 253–281, 1957.
[4] R. D. Banker, A. Charnes, and W. W. Cooper, “Some models for estimating technical and scale inefficiencies in data envelopment analysis,” Management Science, vol. 30, no. 9, pp. 1078–1092, 1984.
[5] A. Charnes, W. W. Cooper, L. Seiford, and J. Stutz, "A multiplicative model for efficiency analysis," Socio-Economic Planning Sciences, vol. 16, no. 5, pp. 223-224, 1982.
[6] A. Charnes, W. W. Cooper, B. Golany, L. Seiford, and J. Stutz, "Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions," Journal of econometrics, vol. 30, no. 1-2, pp. 91-107, 1985.
[7] R. S. Kaplan and D. P. Norton, "The Balanced Scorecard-Measures That Drive Performance," HARVARD BUSINESS REVIEW, p. 71, 1992.
[8] A. Charnes and W. W. Cooper, “Programming with linear fractional functionals,” Naval Research Logistics Quarterly, vol. 9, no. 3-4, pp. 181–186, 1962.
[9] P. Andersen and N. C. Petersen, “A procedure for ranking efficient units in data envelopment analysis,” Management Science, vol. 39, no. 10, pp. 1261–1264, 1993.
[10] F. Hosseinzadeh Lotfi, G. R. Jahanshahloo, M. Khodabakhshi, M. Rostamy-Malkhlifeh, Z. Moghaddas, and M. Vaez-Ghasemi, “A review of ranking models in data envelopment analysis,” Journal of Applied Mathematics, vol. 2013, Article ID 492421, 20 pages, 2013.
[11] G. R. Jahanshahloo, A. Memariani, F. H. Lotfi, and H. Z. Rezai, “A note on some of dea models and finding efficiency and complete ranking using common set of weights,” Applied Mathematics and Computation, vol. 166, no. 2, pp. 265–281, 2005.
[12] T. R. Sexton, “Data envelopment analysis: Critique and extensions. Measuring Efficiency: An Assessment of Data Envelopment Analysis,“ Jossey-Bass, 1986.
[13] L. Song and F. Liu, "An improvement in DEA cross-efficiency aggregation based on the Shannon entropy," International Transactions in Operational Research, vol. 25, no. 2, pp. 705-714, 2018.
[14] D. K. Despotis, "Improving the discriminating power of DEA: Focus on globally efficient units," Journal of the Operational Research Society, vol. 53, no. 3, pp. 314-323, 2002.
[15] J. Wu, J. Sun, and L. Liang, "DEA cross-efficiency aggregation method based upon Shannon entropy," International Journal of Production Research, vol. 50, no. 23, pp. 6726-6736, 2012.
[16] J. Wu, L. Liang, and F. Yang, "Determination of the weights for the ultimate cross efficiency using Shapley value in cooperative game," Expert Systems with Applications, vol. 36, no. 1, pp. 872-876, 2009.
[17] Y.-M. Wang and S. Wang, "Approaches to determining the relative importance weights for cross-efficiency aggregation in data envelopment analysis," Journal of the Operational Research Society, vol. 64, no. 1, pp. 60-69, 2013.
[18] J. Doyle and R. Green, "Efficiency and cross-efficiency in DEA: Derivations, meanings and uses," Journal of the operational research society, vol. 45, pp. 567-578, 1994.
[19] M. Oral, O. Kettani, and P. Lang, "A methodology for collective evaluation and selection of industrial R&D projects," Management science, vol. 37, no. 7, pp. 871-885, 1991.
[20] C. Kao and S.-N. Hwang, "Efficiency measurement for network systems: IT impact on firm performance," Decision support systems, vol. 48, no. 3, pp. 437-446, 2010.
[21] L. Castelli, R. Pesenti, and W. Ukovich, "A classification of DEA models when the internal structure of the decision making units is considered," Annals of Operations Research, vol. 173, pp. 207-235, 2010.
[22] C. Kao, and S. T. Liu, “ Cross efficiency measurement and decomposition in two basic network systems,” Omega, vol. 83, pp.70-79, 2019.
[23] C. Kao, Network data envelopment analysis: Foundations and extensions. springer, 2016.
[24] J. C. Paradi and H. Zhu, "A survey on bank branch efficiency and performance research with data envelopment analysis," Omega, vol. 41, no. 1, pp. 61-79, 2013.
[25] L. Liang, F. Yang, W. D. Cook, and J. Zhu, "DEA models for supply chain efficiency evaluation," Annals of operations research, vol. 145, pp. 35-49, 2006.
[26] L. Zadeh, "Fuzzy sets," Inform Control, vol. 8, pp. 338-353, 1965.
[27] Lertworasirikul, S. (2002). Fuzzy Data Envelopment Analysis (DEA), Ph.D. Dissertation, Dept. of Industrial Engineering, North Carolina State University.
[28] A. Hatami-Marbini, A. Emrouznejad, and M. Tavana, "A taxonomy and review of the fuzzy data envelopment analysis literature: two decades in the making," European journal of operational research, vol. 214, no. 3, pp. 457-472, 2011.
[29] J. K. Sengupta, "A fuzzy systems approach in data envelopment analysis," Computers & mathematics with applications, vol. 24, no. 8-9, pp. 259-266, 1992.
[30] O. A. Girod, "Measuring technical efficiency in a fuzzy environment," Virginia Polytechnic Institute and State University, 1996.
[31] C. Carlsson and P. Korhonen, "A parametric approach to fuzzy linear programming," Fuzzy sets and systems, vol. 20, no. 1, pp. 17-30, 1986.
[32] P. Guo and H. Tanaka, "Fuzzy DEA: a perceptual evaluation method," Fuzzy sets and systems, vol. 119, no. 1, pp. 149-160, 2001.
[33] P. Guo, H. Tanaka, and M. Inuiguchi, "Self-organizing fuzzy aggregation models to rank the objects with multiple attributes," IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, vol. 30, no. 5, pp. 573-580, 2000.
[34] A. Ebrahimnejad and J. L. Verdegay, "A Survey on Models and Methods for Solving Fuzzy Linear Programming Problems, " Fuzzy Logic in lts 50th Year: New Developments, Directions and Challenges, pp. 327-368, 2016.
[35] R. Ghanbari, K. Ghorbani-Moghadam, N. Mahdavi-Amiri, and B. De Baets, "Fuzzy linear programming problems: models and solutions, " Soft Computing, vol. 24, no. 13, pp. 10043-10073, 2020.
[36] A. Hatami-Marbini, M. Tavana, and A. Ebrahimi, "A fully fuzzified data envelopment analysis model, " International Journal of Information and Decision Sciences, vol. 3, no. 3, pp. 252-264, 2011.
[37] A. P. Singh, and S. P. Yadav, "Development of FFDEA Models to Measure the Performance Efficiencies of DMUs, " International Journal of Fuzzy Systems, vol. 24, no. 3, pp. 1446-1454, 2018.
[38] C. Kao and S.-T. Liu, "Cross efficiency measurement and decomposition in two basic network systems," Omega, vol. 83, pp. 70-79, 2019.
[39] Q. Yu and F. Hou, "A cross evaluation-based measure of super efficiency in DEA with interval data," Kybernetes, 2016.
[40] S.-T. Liu and Y.-C. Lee, "Fuzzy measures for fuzzy cross efficiency in data envelopment analysis," Annals of Operations Research, vol. 300, pp. 369-398, 2021.
[41] J. Fan, J. Lan, J. Zhang, Z. Wang, and M. Wu, "A novel cross-efficiency evaluation method under hesitant fuzzy environment," Journal of Intelligent & Fuzzy Systems, vol. 36, no. 1, pp. 371-383, 2019.
