Stochastic Efficiency Based on a Common Set of Weights in Data Envelopment ‎Analysis

محورهای موضوعی : مجله بین المللی ریاضیات صنعتی

M. GHasemi ¹ (Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.)
M. R. Mozaffari ² (Department of Mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran.)
M. Rostamy Malkhalifeh ³ (Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.)
M. H. Behzadi ⁴ (Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.)

تاریخ دریافت : 1399/08/08 تاریخ پذیرش : 1400/05/20 تاریخ انتشار : 1401/01/12

کلید واژه: Common set of weights, Quadratic programming, Stochastic efficiency, Data Envelopment Analysis, Normal Distribution,

چکیده مقاله :

This manuscript extends the CSW model to stochastic inputs and outputs. Next, the stochastic CSW model is transformed into a nonlinear model, and then, the deterministic model is transformed into a quadratic programming model. Finally, the concept presented in this article is demonstrated through a numerical example involving a number of Iranian banks.

چکیده انگلیسی:

تحلیل پوششی داده ها (DEA) روشی برای ارزیابی عملکرد مجموعه ای از واحدهای تصمیم گیرنده (DMU) متجانس با چندین ورودی و چندین خروجی می باشد. . مدل های مختلفی برای محاسبه کارایی در DEA وجود دارند که یکی از آن ها، مدل مجموعه وزن های مشترک (CSW) می باشد، که به طور گسترده ای توسط افراد و متخصصان DEA مورد استفاده قرار می گیرد. در تحلیل پوششی داده های کلاسیک تمام مقادیر ورودی ها و خروجی ها به طور دقیق مشخص می باشند. با این حال این فرض ممکن است در مسائل کاربردی همواره برقرار نباشد. یکی از روش های مهم برای مقابله با داده های نامشخص، بررسی داده های تصادفی در DEA است. این مقاله مدل مجموعه وزن های مشترک را برای حالتی که ورودی ها و خروجی ها تصادفی هستند، توسعه می دهد. سپس مدل تصادفی وزن مشترک (SCSW) به یک مدل قطعی غیر خطی تبدیل می گردد. پس از آن مدل قطعی به یک مدل برنامه ریزی درجه دوم تبدیل می شود. . کارایی به دست آمده با استفاده از داده های تصادفی را کارایی تصادفی می نامیم. مفهوم ارائه شده در این مقاله با مثال عددی که مربوط به شعبه های یک بانک ایرانی است نشان داده می شود.

منابع و مأخذ:

 [1] A. Azadeh, S. Motevali Haghighi, M. Zarrin, S. Khaefi, Performance evaluation of Iranian electricity distribution units by using stochastic data envelopment analysis, International Journal of Electrical Power & Energy Systems 73 (2015) 919-931.
[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) 1078-1092.
[3] A. Charnes, W. W. Cooper, Programming with linear fractional functionals, Naval Research logistics quarterly 9 (1962) 181-186.
[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] A. Charnes, W. Cooper, Q. L. Wei, Z. Huang, Cone ratio data envelopment analysis and multi-objective programming, International Journal of Systems Science 20 (1989) 1099-1118.
[6] W. D. Cook, Y. Roll, A. Kazakov, A Dea Model For Measuring The Relative Eeficiency Of Highway Maintenance Patrols, INFOR: Information Systems and Operational Research 28 (1990) 113-124.
[7] W. D. Cook, J. Zhu, Within-group common weights in DEA: An analysis of power plant efficiency, European Journal of Operational Research 178 (2007) 207-216.
[8] W. W. Cooper, H. Deng, Z. Huang, S. X. Li, Chance constrained programming approaches to congestion in stochastic data envelopment analysis, European Journal of Operational Research 155 (2004) 487-501.
[9] W. W. Cooper, H. Deng, Z. Huang, S. X. Li, Chance constrained programming approaches to technical efficiencies and inefficiencies in stochastic data envelopment analysis, Journal of the Operational Research Society 53 (2002) 1347-1356.
[10] 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.
[11] W. W. Cooper, Z. Huang, S. X. Li, Satisficing DEA models under chance constraints, Annals of operations research 66 (1996) 279-295.
[12] A. Davoodi, H. Z. Rezai, Common set of weights in data envelopment analysis: a linear programming problem, Central European Journal of Operations Research 20 (2012) 355-365.
[13] M. J. Farrell, The Measurement of Productive Efficiency, Journal of the Royal Statistical Society. Series A (General) 120 (1957) 253-290.
[14] F. Hosseinzadeh Lot, G. R. Jahanshahloo, A. Memariani, A Method for Finding Common Set of Weights by Multiple Objective programming in Data Envelopment Analysis, Southwest Journal of Pure and Applied Mathematics 1 (2000) 44-54.
[15] F. Hosseinzadeh Lotfi, N. Nematollahi, M. H. Behzadi, M. Mirbolouki, Z. Moghaddas, Centralized resource allocation with stochastic data, Journal of Computational and Applied Mathematics 236 (2012) 1783-1788.
[16] Z. Huang, S. X. Li, Dominance stochastic models in data envelopment analysis, European Journal of Operational Research 95 (1996) 390-403.
[17] G. R. Jahanshahloo, A. Memariani, F. H. Lotfi, 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 166 (2005) 265-281.
[18] M. Khodabakhshi, An output oriented super-efficiency measure in stochastic data envelopment analysis: Considering Iranian electricity distribution companies, Computers & Industrial Engineering 58 (2010) 663-671.
[19] M. Khodabakhshi, Super-efficiency in stochastic data envelopment analysis: An input relaxation approach, Journal of Computational and Applied Mathematics 235 (2011) 4576-4588.
[20] M. Khodabakhshi, Y. Gholami, H. Kheirollahi, An additive model approach for estimating returns to scale in imprecise data envelopment analysis, Applied Mathematical Modelling 34 (2010) 1247-1257.
[21] F. H. Lotfi, N. Nematollahi, M. Behzadi, M. Mirbolouki, Ranking decision making units with stochastic data by using coefficient of variation, Mathematical and Computational Applications 15 (2010) 148-155.
[22] S. Ramezani-Tarkhorani, M. Khodabakhshi, S. Mehrabian, F. Nuri-Bahmani, Ranking decision-making units using common weights in DEA, Applied Mathematical Modelling 38 (2014) 3890-3896.
[23] Y. Roll, W. D. Cook, B. Golany, Controlling factor weights in data envelopment analysis, IIE transactions 23 (1991) 2-9.
[24] Y. Roll, B. Golany, Alternate methods of treating factor weights in DEA, OMEGAOXFORD-PERGAMON PRESS 21 (1993) 99-99.
[25] M. Tamiz, D. Jones, C. Romero, Goal programming for decision making: An overview of the current state-of-the-art, European Journal of Operational Research 111 (1998) 569-581.
[26] R. Thompson, W. Lesso, R. R. Pettit, C. Samson, L. H. Sterm, F. D. Singleton, B. A. Smith, R. M. Thrall, Systems Task Force
Comparative Site Evaluations for the Texas SSC Project: vol, E and Appendices, Hoston Area Research Center, Woodlands, TX. 1985.
[27] R. G. Thompson, F. Singleton Jr, R. M. Thrall, B. A. Smith, Comparative site evaluations for locating a high-energy physics lab in Texas, Interfaces 16 (1986) 35-49.