A New Practical Common Weights Approach to Rank Decision-Making Units in Data Envelopment Analysis
الموضوعات : 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.
الکلمات المفتاحية: Data Envelopment Analysis, Efficiency, Common set of weights, Ranking, Multiple inputs and outputs,
ملخص المقالة :
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.
[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.
