Table 1.

Definition of variables used in DNDEA model

Variable	Definition
$x_{\mathit{ijk}}^t$	An input resource i to DMUj for the sub-division k at period t
$y_{\mathit{rjk}}^t$	An output product r from DMUj for the sub-division k at period t
$z_{j{\left(\mathit{kh}\right)}_l}^t$	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
$s_{\mathit{iok}}^{t-}$	A slack of the input i of DMUo for sub-division k at period t
$s_{\mathit{rok}}^{t+}$	A slack of the output r of DMUo for sub-division k at period t
$s_{o{\left(\mathit{kh}\right)}_l\alpha }^t$	A slack of link(kh)l of DMUo at period t. α stands for free, " as input " and " as output"
$s_{{\mathit{ok}}_l\alpha }^{\left(t,t+1\right)}$	A slack of carry-over variable kl from period t to period t + 1. α stands for free, good and bad
${\lambda }_{\mathit{jk}}^t$	An intensity of the DMUj corresponding to sub-division k at period t
$s_{{\mathit{ok}}_l\mathit{\text{good}}}^{\left(t,t+1\right)};s_{{\mathit{ok}}_l\mathit{bad}}^{\left(t,t+1\right)};\text{and}{s}_{{\mathit{ok}}_l\mathit{\text{free}}}^{\left(t,t+1\right)}$	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.

Source: Prepared by authors