Uncertain BCC Data Envelopment Analysis Model with Belief Degree: A case study in Iranian Banks

محورهای موضوعی : مجله بین المللی ریاضیات صنعتی

M. Jamshidi ¹ ( Department of Mathematics, Central Tehran Branch, Islamic Azad University, Central Tehran, Iran. )
M. Sanei ² ( Department of Mathematics, Central Tehran Branch, Islamic Azad University, Central Tehran, Iran. )
A. Mahmoodirad ³ ( Department of Mathematics, Masjed-Soleiman Branch, Islamic Azad University, Iran. )
G. Tohidi ⁴ ( Department of Mathematics, Central Tehran Branch, Islamic Azad University, Central Tehran, Iran. )
F. Hosseinzade Lotfi ⁵ ( Department of Mathematics, Science and Rsearch Branch, Islamic Azad University, Tehran, Iran. )

تاریخ دریافت : 1398/12/27 تاریخ پذیرش : 1399/10/29 تاریخ انتشار : 1400/04/10

کلید واژه: BCC model, Iranian ‎Banks, Data Envelopment Analysis, Belief degree, Uncertainty, uncertainty theory,

چکیده مقاله :

The BCC model is studied in this paper in an uncertain environment where uncertain inputs and outputs were belief degree-based uncertainty‚ useful for the cases for which no historical information of an uncertain event is available. As the solution method‚ the uncertain BCC model was converted to a crisp form using two approaches, separately. Finally, an applied example regarding the Iranian Banking system is presented to document the proposed models.

چکیده انگلیسی:

تحلیل پوششی داده ها (DEA) به عنوان یک ابزار تحلیلی قوی که در اندازه گیری کارایی نسبی گروهی از واحدهای تصمیم گیرنده (DMUs) با  چندین ورودی ها و خروجی ها مورد استفاده قرار می گیرد، شناخته می شود. مدلهای DEA به ورودی ها و خروجی هایی با اطلاعات دقیق نیاز دارند. با این حال، در شرایط دنیای واقعی،  ورودی ها و خروجی ها ممکن است ناپایدار و پیچیده باشند،  بنابراین نمی توان به طور دقیق آنها را اندازه گیری کرد. این مسأله منجر به بررسی مدلهای  DEA  نایقین می شود. مدل BCC که در این مقاله مورد مطالعه قرار می گیرد،  در یک محیط نایقین مورد مطالعه قرار گرفته است که در آن ورودی ها و خروجی های نایقین، مبتنی بر درجه باور هستند که  برای مواردی که هیچ اطلاعات تاریخی از یک رویداد نامشخص در دسترس نیست ، مفید می باشند. به عنوان یک روش جواب، مدل BCC نایقین، به طور جداگانه به یک مدل قطعی با استفاده از روشهای مقدار مورد انتظار (EV) و روش محدودیت شانس و مقدار مورد انتظار (EVCC) تبدیل می شود.  سرانجام ، یک مثال کاربردی در مورد سیستم بانکی ایران برای شرح روش پیشنهادی ارائه شده است.

منابع و مأخذ:

[1] A. I. Ali, L. M. Seiford, Translation Invariance in data envelopment analysis, Operations Research Letters 9 (1990) 403-405.
[2] R. D. Banker, A. Charnes, W. W. Cooper, Some models for estimating technical and scale inefficiencies in data envelopment analysis, Management Science 30 (1984) 1031-1142.
[3] R. D. Banker, Maximum likelihood consistency and data envelopment analysis: A statistical foundation, Management Science 39 (1993) 1265-1273.
[4] A. Charnes, W. W. Cooper, E. Rhodes, Measuring the efficiency of decision making units, European Journal of Operational Research 2 (1978) 429-444.
[5] W. Chen, Y. Wang, P. Gupta, M. K. Mehlawat, A novel hybrid heuristic algorithm for a new  uncertain mean-varianceskewness portfolio selection model with real constraints, Applied Intelligence 11 (2018) 1-23.
[6] W. W. Cooper, Z. Huang, V. Lelas, S. X. Li, O. B. Olesen, Chance constrained programming formulations for stochastic characterizations of efficiency and dominance in DEA, Journal of Productivity Analysis 9 (1998) 53-79.
[7] W. W. Cooper, K. S. Park, J. T. Pastor, RAM: a range adjusted measure of on efficiency for use with additive models and relations to other models and measures in DEA, Journal of Productivity Analysis 11 (1999) 5-24.
[8] W. W. Cooper, K. S. Park, G. Yu, Idea and AR-IDEA: models for dealing with imprecise data in DEA, Management Science 45 (1999) 597-607.
[9] W. W. Cooper, k. S. Park, G. Yu, An illustrative application of idea (imprecise data envelopment analysis) to Korean mobil telecommunication compant, Operations Research 49 (2001) 807-820.
[10] H. Dalman, Entropy-based multi-item solid transportation problems with uncertain  variables, Soft Computing http://doi.org/10.1007/s00500-018-3255-1/.
[11] D. Deprins, L. Simar, H. Tulkens, Measuring labor efficiency in post offices. In: Marchand M. Pestieau P. Tulkens H. (Eds) The performance of public enterprises, Elsevier, Science Publishers Amesterdam (1984) pp. 243-267.
[12] T. Entan, Y. Maeda, H. Tanaka, Dual models of interval DEA and its extension to interval data, European Journal of Operational Research 136 (2002) 32-45.
[13] M. J. Farrell, The measurement of productive efficiency, Journal of the Royal Statistical Society A 120 (1957) 253-281.
[14] S. Grosskopf, Statistical inference and nonparametric efficiency: a selective survey, Journal of Productivity Analysis 7 (1996) 161-176.
[15] P. Guo, H. Tanaka, Fuzzy DEA: a perceptual evaluation method, Fuzzy Sets and System 119 (2001) 149-160.
[16] M. Jamshidi, M. Sanei, A. Mahmoodirad, F. Hoseinzadeh Lotfi, G. Tohidi, Uncertain RUSSEL data envelopment analysis model: A case study in Iranian banks, Journal of Intelligent & Fuzzy Systems 37 (2019) 2937-2951.
[17] C. Kao, S. Liu, Fuzzy efficiency measures in data envelopment analysis, Fuzzy Sets and Systems 113 (2000) 427-437.
[18] S. Lertworasirikul, S. Fang, J. A. Joines, H. L. W. Nuttle, Fuzzy data envelopment analysis (DEA): a possibility approach, Fuzzy Sets and Systems 139 (2003) 379-394.
[19] B. Liu, Uncertain Theory, Springer, Berlin 2nd edition, (2007).
[20] B. Liu, Some research problems in uncertainty theory, Journal of Uncertain System 3  (2009) 3-10.
[21] B. Liu, Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty, Springer, Berlin, (2010).
[22] B. Liu, Why is there a need for uncertainty theory, Journal of Uncertain Systems 6 (2012) 3-10.
[23] W. Lio, B. Liu, Uncertain data envelopment analysis with imprecisely observed inputs and outputs, Fuzzy Optimization and Decision Making 17 (2017) 357-373.
[24] W. Lio, B. Liu, Residual and confidence interval for uncertain regression model with imprecise observations, Journal of Intelligent & Fuzzy Systems, (2018), http://dx.doi.org/10.3233/JIFS-18353/.
[25] A. Mahmoodirad, R. Dehghan, S. Niroomand, Modelling linear fractional transportation problem in belief degree-based uncertain environment, Journal of Experimental & Theoretical Intelligence 31 (2019) 393-408.
[26] S. Majumder, P. Kundu, S. Kar, T. Pal, Uncertain multi-objective multi-item fixed charge solid transportation problem with budget constraint, Soft Computing (2018).
[27] O. Olsen, N. C. Petersen, Chance constrained efficiency evaluation, Management Science 131 (1995) 442-457.
[28] T. Sueyosh, DEA non-parametric ranking test and index measurement: Slack-adjust DEA and an application to Japanese agriculture cooperative, Omega 27 (1999) 315-326.
[29] J. K. Sengupta, Efficiency measurement in stochastic input-output system, International Journal of Systems Science 13 (1982) 273-287.
[30] K. Tone, A slacks-based measure of efficiency in data envelopment analysis, European Journal of Operational Research 130 (2001) 498-509.
[31] M. Wen, Z. Qin, R. Kang, Y. Yang, Sensitivity and stability analysis of the additive model in uncertain data envelopment analysis, Springer, Berlin, (2014).
[32] J. Zha, M. Bai, Mean-variance model for portfolio optimization with background risk based on uncertainty theory, International Journal of General Systems 47 (2018) 294-312.