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\begin{equation}
\begin{array}{lll}
\min &\{c^{\rm T}x + E_{\omega} Q(x, \omega) \} \vspace*{.2cm}\\
{\rm s.t.} &Ax &= b \vspace*{.2cm}\\
           &x  &\geq 0,
\end{array}
\end{equation}
\vspace*{.4cm}

where\\

\begin{equation}
\begin{array}{llll}
Q(x, \omega) = &\min &q^{\rm T}(\omega) y \vspace*{.2cm}\\
      &{\rm s.t.} &W(\omega) y &= h(\omega) - T(\omega) x \vspace*{.2cm}\\
                 &&y      &\geq 0.
\end{array}
\end{equation}
\vspace*{.4cm}

In the models above $ \omega \in \Omega $, $ (\Omega, {\cal F}, P) $
is a probability space, and the random entries in the various arrays
are represented through affine sums as follows:

\begin{equation}
\left\{
\begin{array}{lll}
q(\omega) &= q^{0} &+ \sum_{j=1}^{L}q^{j} \xi_{j}(\omega) \vspace*{.2cm}\\
h(\omega) &= h^{0} &+ \sum_{j=1}^{L}h^{j} \xi_{j}(\omega) \vspace*{.2cm}\\
T(\omega) &= T^{0} &+ \sum_{j=1}^{L}T^{j} \xi_{j}(\omega) \vspace*{.2cm}\\
W(\omega) &= W^{0} &+ \sum_{j=1}^{L}W^{j} \xi_{j}(\omega) \vspace*{.2cm}\\
\end{array}
\right.
\end{equation}
\vspace{.4cm}

\noindent
with  $ \xi_{j}(\omega), \;j=1,\ldots\,L$ being random variables. \\

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