Table 1 Definition of variables used in DNDEA model
From: Health system efficiency in OECD countries: dynamic network DEA approach
Variable | Definition |
|---|---|
\( {x}_{ijk}^t \) | An input resource i to DMUj for the sub-division k at period t |
\( {y}_{rjk}^t \) | An output product r from DMUj for the sub-division k at period t |
\( {z}_{j{(kh)}_l}^t \) | A linking intermediate product of DMUj from sub-division k to sub-division h at period t |
\( {z}_{j{k}_l}^{\left(t,t+1\right)} \) | A carry−over of DMUj at the sub-division k from period t to period t + 1 |
\( {s}_{iok}^{t-} \) | A slack of the input i of DMUo for sub-division k at period t |
\( {s}_{rok}^{t+} \) | A slack of the output r of DMUo for sub-division k at period t |
\( {s}_{o{(kh)}_l\alpha}^t \) | A slack of link(kh)l of DMUo at period t. α stands for free, " as input " and " as output" |
\( {s}_{ok_l\alpha}^{\left(t,t+1\right)} \) | A slack of carry-over variable kl from period t to period t + 1. α stands for free, good and bad |
\( {\lambda}_{jk}^t \) | An intensity of the DMUj corresponding to sub-division k at period t |
\( {s}_{ok_l good}^{\left(t,t+1\right)};{s}_{ok_l bad}^{\left(t,t+1\right)};\mathrm{and}\ {s}_{ok_l free}^{\left(t,t+1\right)} \) | The slacks denoting, respectively, carry-over shortfall, carry-over excess and carry-over deviation |
ngoodk; nbadk; nfreek | The number of desirable (good), undesirable (bad) and free carry-over variables for each sub-division k. |