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Table 3 Mathematical formulation of the different models and orientations [[27]]

From: On evaluating health centers groups in Lisbon and Tagus Valley: efficiency, equity and quality

Orientation

CRS

VRS

Inputs

Minimizeθ-ε( i = 1 m s i - + r = 1 s s r + ) subject to 1a. j = 1 n λ j x ij + s i - = θ x i 0 with i=1,…,m 2a. j = 1 n λ j y rj - s r + = y r 0 with r=1,…,s 3. λ j ≥0 with j=1,…,n

Minimizeθ-ε( i = 1 m s i - + r = 1 s s r + ) subject to 1a, 2a, 3 and 4. j = 1 n λ j =1

Outputs

Maximizeϕ-ε( i = 1 m s i - + r = 1 s s r + ) subject to 1b. j = 1 n λ j x ij + s i - = x i 0 with i=1,…,m 2b. j = 1 n λ j y rj - s r + =ϕ y r 0 with r=1,…,s 3. λ j ≥0 with j=1,…,n

Maximizeϕ-ε( i = 1 m s i - + r = 1 s s r + ) subject to 1b, 2b, 3 and 4. j = 1 n λ j =1

Non-oriented

Maximize i = 1 m s i - + r = 1 s s r + subject to 1c. j = 1 n λ j x ij + s i - = x i 0 i=1,,m 2c. j = 1 n λ j y rj - s r + = y r 0 r=1,,s 3. λ j ≥0 j=1,…,n

i = 1 m s i - + r = 1 s s r + subject to 1c, 2c, 3 and 4. j = 1 n λ j =1