Ranking efficient DMUs using the infinity norm and virtual inefficient DMU in DEA

Subject Areas : Data Envelopment Analysis

شکراله  زیاری ¹ (Department of Mathematics, Firoozkooh branch, Islamic Azad University, Firoozkooh, Iran)
مناف  شریف زاده ² (Department of Computer, Firoozkooh Branch, Islamic Azad University, Firoozkooh, Iran)

Received: 2016-08-24 Accepted : 2016-10-12 Published : 2016-12-01

Keywords: Data Envelopment Analysis (DEA), Extreme efficient, Ranking, Efficiency,

Abstract :

In many applications, ranking of decision making units (DMUs) is a problematic technical task procedure to decision makers in data envelopment analysis (DEA), especially when there are extremely efficient DMUs. In such cases, many DEA models may usually get the same efficiency score for different DMUs. Hence, there is a growing interest in ranking techniques yet. The purpose of this paper is ranking extreme efficient DMUs in DEA based on exploiting the leave-one out and minimizing the maximum distance between DMU under evaluation and boundary efficient in input and output directions. The proposed method has been able to overcome the lacks of infeasibility and unboundedness in some DEA ranking methods.

References:

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 onthe 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 inefficiencies in data envelopment analysis. Manage. Sci, 30 (9), 1078-1092.

Briec, W.(1998). Hölder Distance Function and Measurement of Technical Efficiency. Journal of Productivity Analysis, 11, 111-131.

Charnes, A.,  Cooper, W.W., &  Li, S. (1989). Using DEA to evaluate relative efficiencies in the economic performance of Chinese-key cities. Socio-Economic Planning Sciences, 23, 325–344.

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, 2007.

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., 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.

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

Khodabakhshia, M., & Aryavash, K. (2012). Ranking all units in data envelopment analysis. Applied Mathematics 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.,  Silkman, R.H., & Hogan, A.J. (1986). Data envelopment analysis: critique and extensions, in: R.H. Silkman (Ed.), Measuring Efficiency: An Assessment of Data Envelopment Analysis. Jossey-Bass, San Francisco, CA, 73–105.

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

Sueyoshi, T. (1999). Data envelopment analysis non-parametric ranking test and index measurement: Slack-adjusted DEA and an application to Japanese agriculture cooperative. Omega Int. Manage. Sci, 27, 315-326.

Tavares, G., Antunes, C.H. (2001). A Tchebycheff DEA Model. Rutcor Research Report .

Thrall, R.M. (1996). Duality, classification and slacks in DEA. Annals of Operations Research, 66, 109–138.

Torgersen, 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.

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

Zhu, J. (1998). Data envelopment analysis vs. principal component analysis: An illustrative study of economic performance of Chinese cities. European Journal of Operational Research, 111, 50-61.

Ziari, M., & Ziari, S.(2016).  Ranking efficient DMUs using the variation coefficient of weights in DEA.Iranian Journal of Optimization, 8 ,867-907.

Ziari, S., &  Raissi, S.(2016). Ranking efficient DMUs using minimizing distance in DEA. J. Ind. Eng. Int, 12, 237-242.