A New Practical Common Weights Approach to Rank Decision-Making Units in Data Envelopment Analysis
محورهای موضوعی : مجله بین المللی ریاضیات صنعتیM. J. Rezaeiani 1 , A. Foroughi 2
1 - Department of Mathematics, University of Qom, Qom, Iran.
2 - Department of Mathematics, University of Qom, Qom, Iran.
کلید واژه: Data Envelopment Analysis, Efficiency, Common set of weights, Ranking, Multiple inputs and outputs,
چکیده مقاله :
There exist several approaches for deriving a common set of weights in data envelopment analysis (DEA) literature. However, most of these approaches are based on complicated models. In this paper, a new practical approach is proposed to provide a common set of weights. The results of the new approach are compared with some of the existing models through several numerical examples.
چند روش برای یافتن وزن‌های مشترک در تاریخچه تحلیل پوششی داده‌ها وجود دارد. اما بیشتر آن‌ها بر اساس مدل‌های پیچیده هستند. در این مقاله، یک روش عملی جدید برای به دست آوردن مجموعه‌ای از وزن‌های مشترک ارائه می‌شود. به کمک چند مثال عددی، نتایج روش جدید با نتایج برخی از روش‌های موجود مقایسه می‌شود.
[1] H. Ahn, L. Neumann, N. V. Novoa, Measuring the relative balance of DMUs, European Journal of Operational Research 221 (2012) 417-423.
[2] P. Andersen, N. C. Petersen, A procedure for ranking efficient units in data envelopment analysis, Management Science 39 (1993) 1261-1264.
[3] A. Charnes, W. W. Cooper, E. Rhodes, Measuring the efficiency of decision making units, European Journal of Operational Research 2 (1978) 429-444.
[4] A. Charnes, W. W. Cooper, Q. L. Wei, Z. M. Huang, Cone ratio data envelopment analysis and multiple objective linear programming, International Journal of Management Science 20 (1989) 1099-1118.
[5] C. I. Chiang, M. J. Hwang, Y. H. Liu, Determining a common set of weights in a DEA problem using a separation vector, Mathematical and Computer Modelling 54 (2011) 2464-2470.
[6] W. D. Cook, Y. Roll, A. Kazakov, A DEA model for measuring the relative efficiencies of highway maintenance patrols, INFOR 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] J. R. Doyle, R. Green, Efficiency and crossefficiency in DEA: derivations, meanings and uses, Journal of the Operational Research Society 45 (1994) 567-578.
[9] A. A. Foroughi, A new mixed integer linear model for selecting the best decision making units in data envelopment analysis, Computers & Industrial Engineering 60 (2011) 550-554.
[10] A. A. Foroughi, A modified common weight model for maximum discrimination in technology selection, International Journal of Production Research 50 (2012) 3841-3846.
[11] A. A. Foroughi, A revised and generalized model with improved discrimination for finding most efficient DMUs in DEA, Applied Mathematical Modelling 37 (2013) 4067-4074.
[12] L. Friedman, Z. Sinuany-Stern, Scaling units via the canonical correlation analysis in the DEA context, European Journal of Operational Research 100 (1997) 629-637.
[13] G. R. Jahanshahloo, A. Memariani, F. Hosseinzadeh 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.
[14] G. R. Jahanshahloo, F. Hosseinzadeh Lotfi, M. Khanmohammadi, M. Kazemimanesh, V. Rezaie , Ranking of units by positive ideal DMU with common weights, Expert Systems with Applications 37 (2010) 7483-7488.
[15] C. Kao, H. T. Hung, Data envelopment analysis with common weights: the compromise solution approach, Journal of the Operational Research Society 56 (2005) 1196-1203.
[16] E. E. Karsak, S. S. Ahiska, Practical common weight multi-criteria decision-making approach with an improved discriminating power for technology selection, International Journal of Production Research 43 (2005) 1537-1554.
[17] E. E. Karsak, S. S. Ahiska, Improved common weight MCDM model for technology selection, International Journal of Production Research 46 (2008) 6933-6944.
[18] K. Khalili-Damghani, M. Fadaei, A comprehensive common weights data envelopment analysis model: Ideal and anti-ideal virtual decision making units approach, Journal of Industrial and Systems Engineering 11 (2018) 281-306.
[19] F. H. F. Liu, H. H. Peng, Ranking of units on the DEA frontier with common weights, Computers & Operations Research 35 (2008) 1624-1637.
[20] J. S. Liu, L. Y. Y. Lu, W. M. Lu, B. J. Y. Lin, A survey of DEA applications, Omega 41 (2013) 893-902.
[21] 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.
[22] Y. Roll, W. D. Cook, B. Golany, Controlling factor weights in data envelopment analysis, IIE Transactions 23 (1991) 1-9.
[23] N. Ram´on, J. L. Ruiz, I. Sirvent, 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 (2012) 4882-4889.
[24] T. R. Sexton, R. H. Silkman, A. J. Hogan, Data envelopment analysis: critique and extensions, in Measuring Efficiency: An Assessment of Data Envelopment Analysis, Jossey-Bass (1986) 73-105.
[25] J. Shang, T. Sueyoshi, A unified framework for the selection of a flexible manufacturing system, Eoropean Journal of Operational Research 85 (1995) 297-315.
[26] Z. Sinuany-Stern, A. Mehrez, A. Barboy, Academic departments’ efficiency in DEA, Computers and Operations Research 21 (1994) 543-556.
[27] Z. Sinuany-Stern, L. Friedman, DEA and the discriminant analysis of ratios, European Journal of Operational Research 111 (1998) 470-478.
[28] J. Sun, J. Wu, D. Guo, Performance ranking of units considering ideal and anti-ideal DMU with common weights, Applied Mathematical Modelling 37 (2013) 6301-6310.
[29] R. G. Thompson, F. D. Singleton, R. M. Thrall, B. A. Smith, Comparative site evaluations for locating a high-energy physics lab in Texas, Interfaces 16 (1986) 35-49.
[30] M. Toloo, An epsilon-free approach for finding the most efficient unit in DEA, Applied Mathematical Modelling 38 (2014) 3182-3192.
[31] M. Toloo, Alternative minimax model for finding the most efficient unit in data envelopment analysis, Computers & Industrial Engineering 81 (2015) 186-194.
[32] Y. M. Wang, Y. Luo, Y. X. Lan, Common weights for fully ranking decision making units by regression analysis, Expert Systems with Applications 38 (2011) 9122-9128.
[33] Y. M. Wang, P. Jiang, Alternative mixed integer linear programming models for identifying the most efficient decision making unit in data envelopment analysis, Computers & Industrial Engineering 62 (2012) 546-553.
[34] J. Wu, J. Chu, Q. Zhu, Y. Li, L. Liang, Determining common weights in data envelopment analysis based on the satisfaction degree, Journal of the Operational Research Society 67 (2016) 1-13.
[35] A. Yekta, S. Kordrostami, A. Amirteimoori, R. Kazemi Matin, Data envelopment analysis with common weights: the weight restriction approach, Mathematical Sciences 12 (2018) 1-7.
[36] M. Zohrehbandian, A. Makui, A. Alinezhad, A compromise solution approach for finding
common weights in DEA: an improvement to Kao and Hung’s approach, Journal of the Operational Research Society 61 (2010) 604-610.
