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\begin{document}
	\section {Un exemple de document horripilant}
	\subsection{Transportation Approach}
	Next we present a reformulation of the model (1)-(11) using the
	transportation approach. For the reformulation the following
	parameters are defined:
	
	$cs_{ipzu}$: unit cost of production and inventory holding to
	produce a com-
	
	\hspace{1.0cm} ponent $i$ in period $k$ to be mixed in period
	$t$ to satisfy the demand
	
	\hspace{1.0cm} 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:
	
	$ z_{iktl}:$ Amount of component $i$ produced in period $k$, mixed
	in period $t$
	
	\hspace{1.0cm} to satisfy the demand of period $l$.
	
	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}
	
	
\end{document}	
