Ranking Efficient DMUs in Two-stage Network DEA with Common Weights method

Subject Areas : Statistics

M. Ahadzadeh namin ¹ (Department of Mathematics, Shahr-e-Qods Branch, Islamic Azad University,Tehran, Iran.)
E. Khamseh ² (Department of Mathematics, Shahr-e-Qods Branch, Islamic Azad University,Tehran, Iran.)

Received: 2017-05-01 Accepted : 2017-06-29 Published : 2017-10-23

Keywords: تحلیل پوششی داده‌ها (DEA), رتبه‌بندی (Ranking), کارایی, شبکه دو مرحله‌ای, وزن مشترک,

Abstract :

Two stages DEA models are used in many fields of management and industry. One of the concepts that has attracted the attention of researchers in the theory of production is the concept of ranking the units with a two-stage network. A unit ranking can provide useful information to decision makers (DMUs) about optimal decision making activities. This concept defines the superiority of a unit in terms of efficiency and effectiveness on other units. The calculation of the efficiency of the units in the two-stage DEA network was performed, and the efficiency of the two-stage unit could be a suitable criterion for ranking one unit. But the main problem is the time when some efficient units all rank as one. So far, there is no linear model for solving this problem.The purpose of this research is to provide a model for ranking of effecient units using the common weight method in a two-stage DEA network.

References:

 

[1] Andersen, P., Petersen, N. C., (1993), A procedure for ranking efficient units  in data envelopment analysis, Management Science 39, 1261-1264.

 

[2] Banker, R. D., Chang, H., (2006), The super-efficiency procedure for outlier identification, not for ranking efficient units, Euopean Journal of Operation Research 175 (2), 1311-1320.

 

[3] Charnes, A., Cooper, W.W. Rhodes, E., (1987), Measuring the efficiency of decisions making units, European Journal of Operational Research 2, 429-444.

 

[4] Chen, Y., (2004) Ranking efficient units in DEA, Omega 32 (3), 213-219.

 

[5] Chen, Y., Cook, W. D., Li, N., Zho, J. (2009), Additive efficiency decomposition in two stage DEA, European Journal of Operational Research 196, 1170-1176.

 

[6] Chen, Y., Cook, W. D., Zhu, J., (2010), Deriving the DEA frontier for two-stage processes, European Journal of Operational Research 202, 138-142.

 

[7] Chen, Y., Zhu, J., (2004), Measuring Information Technology's Indirect Impact on Firm Performance, Information Technology and Management 5, 9-22.

 

[8] Halkos, G. E., Tzermes, N. G., Kourtzidis, S. A., (2014), A unified classification of two-stage DEA models, Surveys in Operations Research and Management Science 19, 1-16. 

 

[9] Li, S., Jahanshahloo, G.R., Khodabakhshi, M., (2007), A super-efficiency model for ranking efficient units in data envelopment analysis, Applied Mathematics and Computation 184 (2), 638-648. 

 

[10] Liu, F.H.F., Peng, H. H., (2006), Ranking of units on the DEA frontier with common weights, Computer & Operation Research 35, 1624- 1637.

 

[11] Lovell, C. A. K, Rouse, A. P. B., (2003), Equivalent standard DEA models to provide superefficiency scores, Journal of the Operational Reseach Society 54 (1), 101-108.

 

[12] Obata, T., Ishii, H., (2003), A method of discriminating efficient candidates with ranked voting data, European Jouurnal of Operational Research 151, 233-237.

 

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

 

[14] Seiford, L. M., Zhu, J., (1999), Profitability and marketability of the top 55 US commercial banks, Management Science 45 (9), 1270-1288.

 

[15] Sexton, T. R., Silkman, R. H., Hogan, A. J., (1986), Data envelopment analysis; Critique and extensions, in; R. H. Silkman (Ed.), Measuring Efficienency An Assessment of Data Envelopment Analysis, Jossey-Bass, San Francisco, CA, 73-105.