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A new method for ranking non-extreme efficient units in data envelopment analysis

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Abstract

Data envelopment analysis (DEA) evaluates the performance of decision making units (DMUs). When DEA models are used to calculate efficiency of DMUs, a number of them may have the equal efficiency 1. In order to choose a winner among DEA efficient candidates, some methods have been proposed. But most of these methods are not able to rank non-extreme efficient DMUs. Since, the researches performed about ranking of non-extreme efficient units are very limited, incomplete and with some difficulties, we are going to develop a new method to rank these DMUs in this paper. Therefore, we suppose that DMU o is a non-extreme efficient under evaluating DMU. In continue, by using “Representation Theorem”, DMU o can be represented as a convex combination of extreme efficient DMUs. So, we expect the performance of DMU o be similar to the performance of convex combination of these extreme efficient DMUs. Consequently, the ranking score of DMU o is calculated as a convex combination of ranking scores of these extreme efficient DMUs. So, the rank of this unit will be determined.

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Authors and Affiliations

  1. Department of Mathematics, Firoozkooh Branch, Islamic Azad University, Firoozkooh, Iran

    A. Gholam Abri, N. Shoja & M. Fallah Jelodar

  2. Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

    G. R. Jahanshahloo & F. Hosseinzadeh Lotfi

Authors
  1. A. Gholam Abri
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  2. G. R. Jahanshahloo
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  3. F. Hosseinzadeh Lotfi
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  4. N. Shoja
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  5. M. Fallah Jelodar
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Correspondence to A. Gholam Abri.

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Gholam Abri, A., Jahanshahloo, G.R., Hosseinzadeh Lotfi, F. et al. A new method for ranking non-extreme efficient units in data envelopment analysis. Optim Lett 7, 309–324 (2013). https://doi.org/10.1007/s11590-011-0420-1

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  • DOI: https://doi.org/10.1007/s11590-011-0420-1

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