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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.
  1. Source: Prepared by authors