Ali Payan - Department of Mathematics, zahedan Branch, Islamic Azad University, zahedan, Iran
Motahareh Ebrahimzade-Adimi - Department of Mathematics, zahedan Branch, Islamic Azad University, zahedan, Iran

This paper presents a new index for ranking efficient units based on the idea of super efficiency (SE) and common weights (CW) in data envelopment analysis (DEA), by using ideal and anti-ideal virtual units. In DEA models presented for ranking the efficient decision making units (DMUs), the weighted sum of outputs to inputs is considered for the assessment of DMUs. If this ratio will be able recognize the difference among the efficient units, it was done in the classic DEA models. Therefore, the primary purpose of this paper is to introduce a new criterion as a measure to evaluate the efficient DMUs, based on the ideal and anti-ideal units. Then, a CW method is proposed to measure the collective performance of all efficient DMUs based on the defined criterion. The difference between the collective performance in presence and absence of the evaluating DMU is considered as an index for its performance. Finally, an example is presented for further understanding of the proposed method and compared with the related literature.

Data envelopment analysis, common weights, super efficiency