Uncertainty in Data Envelopment Analysis

4.2.3.2: Ranking the DMUs according to the interval cross-efficiency values

As mentioned in the previous section, for a certain cut value the cross-efficiency of DMU_j is represented as ${\left[{\overline{\theta }}_j^L,{\overline{\theta }}_j^U\right]}_{\alpha }$. To rank the DMUs according to the obtained intervals of cross-efficiency values, the method proposed by Wang et al. (2005) is used. This method is based on minimizing the maximum loss and is suitable for comparing the interval values with a common center value.

For DMU_k assume $b=\underset{j\ne k}{max}\left\{{\overline{\theta }}_j^U\right\}$. As ${\overline{\theta }}_k^L<b$, therefore the maximum loss of efficiency $r_k^U=\underset{}{max\; ...}$