Title: Optimising proportional weights as a secondary goal in DEA cross-efficiency evaluation

Authors: Reza Maddahi; Gholam Reza Jahanshahloo; Farhad Hosseinzadeh Lotfi; Ali Ebrahimnejad

Addresses: Department of Mathematics, Science and Research Branch, Islamic Azad University, P.O. Box 14778, Tehran, Iran ' Department of Mathematics, Science and Research Branch, Islamic Azad University, P.O. Box 14778, Tehran, Iran ' Department of Mathematics, Science and Research Branch, Islamic Azad University, P.O. Box 14778, Tehran, Iran ' Department of Mathematics, Qaemshahr Branch, Islamic Azad University, P.O. Box 163, Qaemshahr, Iran

Abstract: Cross-efficiency evaluation is an alternative approach to rank of decision making units (DMUs) in data envelopment analysis (DEA). This approach introduces a cross-efficiency matrix, in which the units are self and peer evaluated. However, the cross-efficiency scores may not be unique due to the presence of alternate optima. To overcome this shortcoming, the secondary goals have been introduced in the cross-efficiency evaluation. In this paper, we propose the proportional weight assignment technique that makes a selection of weight proportional to its corresponding input or output as a secondary goal in DEA cross-efficiency evaluation. A numerical example is solved by use of the proposed method and its results are compared with other approaches. The results show that our proposed method can be effective and practical.

Keywords: data envelopment analysis; DEA; cross-efficiency evaluation; proportional weights; efficiency ranking; decision making units; DMUs.

DOI: 10.1504/IJOR.2014.058953

International Journal of Operational Research, 2014 Vol.19 No.2, pp.234 - 245

Received: 26 Jul 2012
Accepted: 01 Oct 2012
Published online: 17 Jun 2014 *

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