Cross Efficiency Matrix in Non-Radial Models

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Abstract. In data envelopment analysis each decision making unit is analyzed in best situation and in CCR models for the unit under analysis the best weights are considered for inputs and outputs. So, if the decision making unit in its best situation is less than one, it is inefficient, otherwise it is efficient. Therefore, the present article is an attempt to achieve the cross efficiency matrix by using SBM and then rank the decision making units by using the cross efficiency matrix. Overall, selecting the optimal portfolio is done by cross efficiency matrix. In order to find the efficient firms the mean, column variance and covariance of data of cross efficiency scale are utilized. Finally, the cross efficiency matrix of 22 firms with two inputs and one output has been calculated using non-radial models. 


Data Envelopment Analysis, Cross Efficiency Matrix, Non-radial Models

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Andersen, P., Petersen, N. C., (1993). A procedure for ranking efficient units in data envelopment analysis. Management science, 39(10):1261-4.

Doyle JR and R Green (1994). “Efficiency and Cross-Efficiency in DEA: Derivations, Meanings and Uses.” JORS 45(5): 567-578.

F. Hosseinzadeh Lotfi, G. R. Jahanshahloo and M. Esmaeili,(2007). Classification of Decision Making Units with Interval Data Using SBM Model. Department of Mathematics, Azad University Research & Science Branch, Tehran, Iran.

J.T. Pastor, J.L. Ruiz, I. SirventCorresponding author contact information. An enhanced DEA Russell graph efficiency measure. European Journal of Operational Research. Volume 115, Issue 3, 16 June 1999.

Lim, S., Oh, K.W., Zhu, J., Use of DEA Cross-Efficiency Evaluation in Portfolio Selection:An application to Korean Stock Market, European Journal of Operational Research (2013), 10.1016/j.ejor.2013.12.002

Mehrabian, S., Alirezaee, M. R., Jahanshahloo, G. R., (1999). A complete efficiency ranking decision making units in data envelopment analysis", Computational optimization and applications, 4, 261-266.

Saati, S., Zarafat Angizl, M., Memariani, A., Jahanshahloo, G. R., (1999). A model for ranking decision making units in data envelopment analysis, Riceria operative, 31(97).

Thomson, D.J., 1990. Time series analysis of Holocene climate data. Philosophical Transactions of the Royal Society of London, Series A 330, 601-616.

Stewart, T. and others. (1996). Intelletual capital. London. Sage.