Research Article
Malmquist–Luenberger Productivity Index for a Two-Stage Structure in the Presence of Undesirable Outputs and Uncertainty
Table 8
The results of the overall and the stages efficiency scores in 2021.
| | Overall efficiency | First stage | Second stage | value | 0.49 | 0.50 | 0.51 | 0.52 | 0.49 | 0.50 | 0.51 | 0.52 | 0.49 | 0.50 | 0.51 | 0.52 |
| DMUs | | | | | | | | | | | | | 1 | 0.594 | 0.619 | 0.619 | 0.619 | 0.732 | 0.724 | 1.000 | 1.000 | 0.238 | 0.238 | 0.238 | 0.239 | 2 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 3 | 0.748 | 0.858 | 0.858 | 0.859 | 0.515 | 0.594 | 0.831 | 0.831 | INF | 0.845 | 0.846 | 0.845 | 4 | 0.468 | 0.518 | 0.519 | 0.519 | 0.587 | 0.662 | 0.663 | 0.664 | 0.300 | 0.301 | 0.302 | 0.302 | 5 | INF | 0.617 | 0.617 | 0.617 | INF | 0.774 | 0.721 | 0.722 | 0.448 | 0.466 | 0.466 | 0.466 | 6 | 0.758 | 0.857 | 0.859 | 0.859 | 0.577 | 0.627 | 0.531 | 0.532 | 1.000 | 1.000 | 1.000 | 1.000 | 7 | 0.600 | 0.789 | 0.790 | 0.791 | 0.577 | 0.588 | 0.793 | 0.793 | 0.830 | 0.851 | 0.851 | 0.851 | 8 | 0.736 | 0.769 | 0.769 | 0.769 | 0.532 | 0.512 | 0.535 | 0.536 | 0.746 | 0.804 | 0.805 | 0.805 | 9 | INF | 0.852 | 0.853 | 0.854 | 0.942 | 0.929 | 0.723 | 0.723 | 0.733 | 0.896 | 0.897 | 0.897 | 10 | 0.687 | 0.714 | 0.716 | 0.716 | 0.725 | 0.738 | 0.713 | 0.717 | 0.670 | 0.528 | 0.529 | 0.529 | 11 | 0.604 | 0.851 | 0.853 | 0.853 | 0.535 | 0.529 | 0.682 | 0.683 | 0.763 | 0.871 | 0.872 | 0.871 |
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