Table 3.

Optimal solutions: $x_{\mathit{guk}}^{s\theta \ast }$ and $y_{\mathit{ufk}}^{s\theta \ast }$, for all $g,u,k,\widehat{f},\tilde{f},s,\theta$

Variables	Stage	Scenarios		$u=1$	$u=2$	Variables		$u=1$	$u=2$
$x_{\mathit{guk}}^{1\ast }$	$s=1$	I	$\begin{array}{c}g=1\\ g=2\\ g=3\end{array}$	$\begin{array}{c}1.32\\ 1.32\\ 3.99\end{array}$	$\begin{array}{c}0.67\\ 0.67\\ 2.00\end{array}$	$y_{\mathit{uf}}^{1\ast }$	$\begin{array}{c}\widehat{f}=1\\ \widehat{f}=2\\ \tilde{f}=1\\ \tilde{f}=2\end{array}$	$\begin{array}{c}1.24\\ 0.69\\ 1.81\\ 0.71\end{array}$	$\begin{array}{c}2.82\\ 1.73\\ 0.75\\ 0.20\end{array}$
		${\omega }_1$	$\begin{array}{c}g=1\\ g=2\\ g=3\end{array}$	$\begin{array}{c}0.00\\ 1.38\\ 0.00\end{array}$	$\begin{array}{c}0.00\\ 1.61\\ 0.00\end{array}$		$\begin{array}{c}\widehat{f}=1\\ \widehat{f}=2\\ \tilde{f}=1\\ \tilde{f}=2\end{array}$	$\begin{array}{c}0.24\\ 0.66\\ 0.48\\ 0.00\end{array}$	$\begin{array}{c}0.00\\ 0.62\\ 0.00\\ 0.00\end{array}$
$x_{\mathit{guk}}^{2\omega \ast }$	$s=2$	${\omega }_2$	$\begin{array}{c}g=1\\ g=2\\ g=3\end{array}$	$\begin{array}{c}2.64\\ 0.00\\ 4.64\end{array}$	$\begin{array}{c}1.35\\ 0.00\\ 2.35\end{array}$	$y_{\mathit{uf}}^{2\omega \ast }$	$\begin{array}{c}\widehat{f}=1\\ \widehat{f}=2\\ \tilde{f}=1\\ \tilde{f}=2\end{array}$	$\begin{array}{c}1.37\\ 3.08\\ 1.98\\ 0.84\end{array}$	$\begin{array}{c}0.78\\ 1.89\\ 0.79\\ 0.25\end{array}$
		${\omega }_3$	$\begin{array}{c}g=1\\ g=2\\ g=3\end{array}$	$\begin{array}{c}6.44\\ 5.11\\ 6.44\end{array}$	$\begin{array}{c}5.55\\ 4.88\\ 5.55\end{array}$		$\begin{array}{c}\widehat{f}=1\\ \widehat{f}=2\\ \tilde{f}=1\\ \tilde{f}=2\end{array}$	$\begin{array}{c}2.66\\ 3.33\\ 6.58\\ 5.42\end{array}$	$\begin{array}{c}2.33\\ 2.66\\ 5.92\\ 5.08\end{array}$
		${\xi }_1$	$\begin{array}{c}g=1\\ g=2\\ g=3\end{array}$	$\begin{array}{c}0.69\\ 1.36\\ 2.02\end{array}$	$\begin{array}{c}0.31\\ 0.64\\ 0.98\end{array}$		$\begin{array}{c}\widehat{f}=1\\ \widehat{f}=2\\ \tilde{f}=1\\ \tilde{f}=2\end{array}$	$\begin{array}{c}0.73\\ 1.80\\ 1.12\\ 0.41\end{array}$	$\begin{array}{c}0.37\\ 1.09\\ 0.40\\ 0.05\end{array}$
		${\xi }_2$	$\begin{array}{c}g=1\\ g=2\\ g=3\end{array}$	$\begin{array}{c}1.34\\ 0.67\\ 3.34\end{array}$	$\begin{array}{c}0.66\\ 0.32\\ 1.66\end{array}$		$\begin{array}{c}\widehat{f}=1\\ \widehat{f}=2\\ \tilde{f}=1\\ \tilde{f}=2\end{array}$	$\begin{array}{c}0.99\\ 2.31\\ 1.47\\ 0.58\end{array}$	$\begin{array}{c}0.54\\ 1.40\\ 0.56\\ 0.13\end{array}$
		${\xi }_3$	$\begin{array}{c}g=1\\ g=2\\ g=3\end{array}$	$\begin{array}{c}2.57\\ 0.57\\ 4.57\end{array}$	$\begin{array}{c}1.43\\ 0.43\\ 2.43\end{array}$		$\begin{array}{c}\widehat{f}=1\\ \widehat{f}=2\\ \tilde{f}=1\\ \tilde{f}=2\end{array}$	$\begin{array}{c}1.47\\ 3.27\\ 2.09\\ 0.89\end{array}$	$\begin{array}{c}0.89\\ 2.12\\ 0.94\\ 0.32\end{array}$
$x_{\mathit{guk}}^{3\xi \ast }$	$s=3$	${\xi }_4$	$\begin{array}{c}g=1\\ g=2\\ g=3\end{array}$	$\begin{array}{c}0.69\\ 1.36\\ 2.02\end{array}$	$\begin{array}{c}0.31\\ 0.64\\ 0.97\end{array}$	$y_{\mathit{uf}}^{3\xi \ast }$	$\begin{array}{c}\widehat{f}=1\\ \widehat{f}=2\\ \tilde{f}=1\\ \tilde{f}=2\end{array}$	$\begin{array}{c}0.73\\ 1.80\\ 1.12\\ 0.41\end{array}$	$\begin{array}{c}0.38\\ 1.08\\ 0.41\\ 0.05\end{array}$
		${\xi }_5$	$\begin{array}{c}g=1\\ g=2\\ g=3\end{array}$	$\begin{array}{c}2.62\\ 2.62\\ 3.69\end{array}$	$\begin{array}{c}1.37\\ 1.37\\ 2.04\end{array}$		$\begin{array}{c}\widehat{f}=1\\ \widehat{f}=2\\ \tilde{f}=1\\ \tilde{f}=2\end{array}$	$\begin{array}{c}1.79\\ 3.74\\ 2.55\\ 1.13\end{array}$	$\begin{array}{c}1.06\\ 2.26\\ 1.08\\ 0.39\end{array}$
		${\xi }_6$	$\begin{array}{c}g=1\\ g=2\\ g=3\end{array}$	$\begin{array}{c}4.77\\ 4.11\\ 6.11\end{array}$	$\begin{array}{c}2.22\\ 1.88\\ 2.88\end{array}$		$\begin{array}{c}\widehat{f}=1\\ \widehat{f}=2\\ \tilde{f}=1\\ \tilde{f}=2\end{array}$	$\begin{array}{c}3.16\\ 4.33\\ 5.1\\ 2.4\end{array}$	$\begin{array}{c}1.83\\ 1.66\\ 2.43\\ 1.07\end{array}$
		${\xi }_7$	$\begin{array}{c}g=1\\ g=2\\ g=3\end{array}$	$\begin{array}{c}5.73\\ 5.53\\ 5.73\end{array}$	$\begin{array}{c}2.58\\ 2.48\\ 2.58\end{array}$		$\begin{array}{c}\widehat{f}=1\\ \widehat{f}=2\\ \tilde{f}=1\\ \tilde{f}=2\end{array}$	$\begin{array}{c}3.28\\ 4.56\\ 6.20\\ 2.95\end{array}$	$\begin{array}{c}1.71\\ 1.44\\ 3.08\\ 1.39\end{array}$
		${\xi }_8$	$\begin{array}{c}g=1\\ g=2\\ g=3\end{array}$	$\begin{array}{c}5.65\\ 5.65\\ 5.65\end{array}$	$\begin{array}{c}2.56\\ 2.56\\ 2.56\end{array}$		$\begin{array}{c}\widehat{f}=1\\ \widehat{f}=2\\ \tilde{f}=1\\ \tilde{f}=2\end{array}$	$\begin{array}{c}3.29\\ 4.52\\ 6.18\\ 2.96\end{array}$	$\begin{array}{c}1.71\\ 1.47\\ 3.13\\ 1.39\end{array}$