Malmquist–Luenberger Productivity Index for a Two-Stage Structure in the Presence of Undesirable Outputs and Uncertainty

Table 12

MPI for the overall process and the first and the second stages.

DMUs	Overall process 2020-2021			First stage 2020-2021			Second stage 2020-2021
	EC	TC	MPI	EC	TC	MPI	EC	TC	MPI
1	0.619	1.042	0.645	0.724	4.155	3.008	0.238	45.667	10.869
2	1.000	1.170	1.170	1.000	1.000	1.000	1.000	1.993	1.993
3	0.858	1.365	1.171	0.594	0.847	0.503	0.845	1.114	0.941
4	0.518	2.107	1.091	0.901	1.054	0.950	0.456	9.587	4.372
5	0.617	1.408	0.869	0.638	1.252	0.799	0.623	1.471	0.916
6	0.857	2.155	1.847	0.876	0.319	0.279	1.353	0.860	1.164
7	0.789	0.492	0.388	0.809	0.537	0.434	1.025	0.988	1.013
8	0.769	1.315	1.011	0.698	1.197	0.836	1.438	0.163	0.234
9	0.852	1.416	1.206	1.036	1.729	1.791	1.219	4.134	5.039
10	0.714	3.858	2.755	0.738	0.612	0.452	0.783	2.765	2.165
11	0.851	1.108	0.943	0.637	2.938	1.872	0.871	0.529	0.461
Average	0.768	1.585	1.191	0.786	1.422	1.084	0.896	6.297	2.652