Ranking efficient DMUs using the variation coefficient of weights in DEA

Subject Areas : Data Envelopment Analysis

Mojtaba  Ziari ¹ (Member of young researchers and elite club, Firoozkooh branch, Islamic Azad University, Firoozkooh, Iran)
Shokrollah  Ziari ² (Department of Mathematics, Firoozkooh branch, Islamic Azad University, Firoozkooh, Iran)

Received: 2016-02-22 Accepted : 2016-04-12 Published : 2016-06-01

Keywords: Data Envelopment Analysis (DEA), Ranking, Extreme efficient, Coefficient of variation,

Abstract :

One of the difficulties of Data Envelopment Analysis(DEA) is the problem of de_ciency discrimination among efficient Decision Making Units(DMUs) and hence, yielding large number of DMUs as efficient ones. The main purpose of this paper is to overcome this inability. One of the methods for ranking efficient DMUs is minimizing the Coefficient of Variation (CV) for inputs-outputs weights. In this paper, it is introduced a nonlinear model for ranking efficient DMUs based on the minimizing the mean absolute deviation of weights and then we convert the nonlinear model proposed into a linear programming form.

References:

Adler, N., Friedman, L.,  & Sinuany-Stern, Z. (2002). Review of ranking methods in the data envelopment analysis context. European Journal of Operational Research, 140, 249-265.

Amirteimoori, A., Jahanshahloo, G.R., & Kordrostami ,S. (2005). Ranking of decision making units in data envelopment analysis: A distance-based approach, Applied Mathematics and Computation, 171,122-135.

Andersen, P., & Petersen, N.C. (1993). A procedure for ranking efficient units in data envelopment analysis. Manage. Sci, 39, 1261-1264.

Bal, H., orkcu, H. H.,  & Celebioglu, S. (2008). A new method based on the dispersion of weights in data envelopment analysis. Journal of Computers Industrial Engineering, 54, 502-512.

Banker, R.D.,Charnes, A., & Cooper, W.W. (1984). Some methods for estimating technical and scale inefficienciesin data envelopment analysis. Manage. Sci, 30 (9), 1078-1092.

Charnes, A., Cooper, W.W., &  Rhodes, E. (1978). Measuring the efficiency of decision making units. Eur.J. Oper.Res,2 (6), 429-444.

 

Cooper, W. W.,Seiford, L. M., & Tone, K.(2007). Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-solver Software, Second Edition, Spriger.

Hashimato, A.(1999). A ranked voting system using a DEA/AR exclusion model:A note, Eur. J. Oper.Res,97, 600-604.

Jahanshahloo, G.R.,Hosseinzadeh Lotfi, F., Shoja, N., & Tohidi, G., Razavian, S.(2004). Ranking by using L1-norm in data envelopment analysis. Appl. Math.Comput. 153, 215-224.

Jahanshahloo, G.R. , Sanei, M., Hosseinzadeh Lotfi, F.,  & Shoja, N. (2004). Using the gradient line for ranking DMUs in DEA. Applied Mathematics and Computation, 151, 209-219.

Jahanshahloo, G.R. , & Firoozi Shahmirzadi, P.(2013). New methods for ranking decision making units based on the dispersion of weights and Norm 1 in data envelopment analysis. Computers & Industrial Engineering, 65, 187-193.

Khodabakhshi, M., & Aryavash, K.(2012). Ranking all units in data envelopment analysis. Applied Math-ematics Letters, 25, 2066-2070.

Liu, F. F., & Peng, H. H.(2008). Ranking of units on the DEA frontier with common weights. Computers & Operations Research, 35, 1624-1637.

Mehrabian, S., Alirezaee, M.R., & Jahanshahloo, G.R.(1999). A compelete efficiency ranking of decision making units in data envelopment analysis. Comput.Optimiz. Appl,14, 261-266.

Rezai Balf, F.,Zhiani Rezai, H., Jahanshahloo, G.R., &  Hosseinzadeh Lotfi, F.(2012). Ranking efficient DMUs using the Tchebycheff norm. Applied Mathematical Modelling ,36, 46-56.

Seiford, L. M., & Zhu, J.(1999). Infeasibility of super-efficiency data envelopment analysis models. INFOR ,37 (2), 174-187.

Sexton, T. R. (1986).The methodology of data envelopment analysis. In R. H.Silkman (Ed.), Measuring efficiency: An assessment of data envelopment analysis, San Fransisco, Jossey-Bass, 7-29.

Shetty, U. , & Pakkala, T. P. M.(2010). Ranking efficient DMUs based on single virtual DMU in DEA.Operational Research Society, 47(1), 20-72.

Torgesen, A. M., Forsund, F. R., & Kittelsen, S.A.C.(1996). Slack-adjusted efficiency measures and ranking of efficient units, The J. Prod.Anal, 7, 379-398.

Wua, J., & Yan, H.(2010). An effective transformation in ranking using l1-norm in data envelopment analysis. Applied Mathematics and Computation ,217, 4061-4064.