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\begin{document}
	\section {Un exemple de document horripilant}
\subsection{Portation Approach}
Next we present a reformulation of the model (1)--(11) using the
portation approach. For the reformulation the following
parameters are defined:
\begin{description}
\item $cs_{ipzu}$: unit cost of production and inventory holding to produce a component $i$ in period $k$ to be mixed in period
$t$ to satisfy the demand
of period $l$;
$$cz_{ipts} = vc_{jf} + vc^E_t +\displaystyle\sum_{s=k}^{t-1}hc_{is} + \displaystyle\sum_{b=t}^{l-3}hc^E_j $$
We also define new variables for the model:

\item $ z_{iktl}:$ Amount of component $i$ produced in period $k$, mixed
in period $t$
to satisfy the demand of period~$l$.
\end{description}

The reformulation based on the transportation problem $(F2)$ is as
follows:
%%%%
\begin{eqnarray}\label{objeti}
\displaystyle\hspace{0cm}Min\displaystyle\sum_{t=1
}^msc^E_{t}y^E_{t}+\displaystyle\sum_{t=1
}^m\sum_{i=1}^nsc_{it}y_{it} +
\displaystyle\sum_{i=1}^n\displaystyle\sum_{k=1}^m\displaystyle\sum_{t=k}^m\displaystyle\sum_{l=t}^mcs_{iktl}z_{iktl}
\hspace{0.2cm}\end{eqnarray} \hspace{0.8cm}Subject
to:\vspace*{0.1cm}
\begin{eqnarray}
&\displaystyle\sum_{i=1}^n\displaystyle\sum_{k=1}^l\displaystyle\sum_{t=k}^lz_{iktl}=d^E_{l} \hspace{7.0cm} \forall{l\in T}& \label{bala}\\
&\displaystyle\sum_{i=1}^n\displaystyle\sum_{k=1}^tz_{iktl}\leq d^E_{l}y^E_{t}\hspace{6.1cm} \forall{t,l\in T,l\geq t}&\label{prepar} \\
&st^E_{t}y^E_{t}+
\displaystyle\sum_{i=1}^n\displaystyle\sum_{k=1}^t\displaystyle\sum_{l=t}^mvt^E_tz_{iktl}\leq
Cap^E_{t}\hspace{4.2cm}\forall{t\in T}&\label{capacidad}\\
\end{eqnarray}
	
	
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