DEA-NETWORK-SBM - Network Slacks-Based Measure DEA with Window Analysis

1. 1. Validate complete stage-period panel and define windows

   $$W_p=\{(j,t):j=1,\dots ,n;t=p,\dots ,p+w-1\};p=1,\dots ,T-w+1$$

2. 2. Solve VRS free-link SBM for every DMU-period in each window

   $${\eta }_{o,t|p}=\min \frac{1-{\sum }_k{\omega }_k{m}_k^{-1}{\sum }_i{s}_{ik}^{-}/x_{o,t,ik}}{1+{\sum }_k{\omega }_k{r}_k^{-1}{\sum }_r{s}_{rk}^{+}/y_{o,t,rk}};X_{W_p}^k{\lambda }^k+s_k^{-}=x_{o,t}^k;Y_{W_p}^k{\lambda }^k-s_k^{+}=y_{o,t}^k;1^T{\lambda }^k=1;Z_{W_p}^{fh}{\lambda }^f=Z_{W_p}^{fh}{\lambda }^h;\lambda ,s^{-},s^{+}\ge 0$$

3. 3. Compute stage efficiencies and aggregate period scores

   $${\tau }_{o,t|p,k}=\frac{1-m_k^{-1}{\sum }_i{s}_{ik}^{-}/x_{o,t,ik}}{1+r_k^{-1}{\sum }_r{s}_{rk}^{+}/y_{o,t,rk}};{\bar{\eta }}_{o,t}=\frac{{\sum }_{p:t\in W_p}{\eta }_{o,t|p}}{|\{p:t\in W_p\}|};{\bar{\eta }}_o=T^{-1}\sum _t{\bar{\eta }}_{o,t}$$