Finding the strong defining hyperplanes of production possibility set with constant returns to scale using the linear independent vectors

Figures & data

Table 1. Data set for the numerical Example 4.1

	${\text{DMU}}_A$	${\text{DMU}}_B$	${\text{DMU}}_C$	${\text{DMU}}_D$	${\text{DMU}}_E$	${\text{DMU}}_F$	${\text{DMU}}_G$	${\text{DMU}}_F$
x	2	3	3	4	5	5	6	8
y	1	3	2	3	4	2	3	5

Figure 1. Numerical Example 4.1.

Table 2. The obtained results based on model (5): Data set for the numerical Example 4.1

Variables	${\text{DMU}}_A$	${\text{DMU}}_B$	${\text{DMU}}_C$	${\text{DMU}}_D$	${\text{DMU}}_E$	${\text{DMU}}_F$	${\text{DMU}}_G$	${\text{DMU}}_H$
z	0.5000000	1.0000000	0.6666666	0.7500000	0.8000000	0.4000000	0.5000000	0.6250000
$u_1$	0.5000000	0.3333333	0.3333333	0.2500000	0.2000000	0.2000000	0.1666667	0.1250000
$v_1$	0.5000000	0.3333333	0.3333333	0.2500000	0.2000000	0.2000000	0.1666667	0.1250000
$l_1^1$	1.0000000	1.0000000	1.0000000	1.0000000	1.0000000	1.0000000	1.0000000	1.0000000

Table 3. Data set for the numerical Example 4.2

	${\text{DMU}}_A$	${\text{DMU}}_B$	${\text{DMU}}_C$	${\text{DMU}}_D$
$x_1$	1	2	5	6
$x_2$	4	2	1	5
$y_1$	1	1	1	1

Figure 2. Numerical Example 4.2.

Table 4. The obtained results based on model (5): Data set for the numerical Example 4.2

Variables	${\text{DMU}}_A$	${\text{DMU}}_B$	${\text{DMU}}_C$	${\text{DMU}}_D$
z	1.0000000	1.0000000	1.0000000	0.3809524
$v_1$	0.3333333	0.3333333	0.1250000	0.0476190
$v_2$	0.1666667	0.1666667	0.3750000	0.1428571
$u_1$	1.0000000	1.0000000	1.0000000	0.3809524
$t_1^1$	0.3333333	0.3333333	0.1250000	0.1250000
$t_1^2$	0.1666667	0.1666667	0.3750000	0.3750000