First, we denote this:
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And we get this right property( $last_i$ means the last node on $τ_i$):
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$Smin_i^h$ = $\sum_{h'=first_i}^{h-1} ({C_i^{h'} + L_{max})}$

$Smax_i^h$ = $W_{i,t}^{h-1}$ + $C_i^{h-1}$ + $L_{max}$

In this case, the values are simple:
$C_i^h$ = 4, for all values of $i$ or $h$.
$L_{max}$ = $L_{min}$ = 1.
$T_{i}$ = 36, for all values of $i$.
$J_i$ = 0, for all values of $i$.
{$τ_1$, $τ_2$, ... , $τ_n$}, the set of all flows.
$n$ = 5, the total number of flows.

And the flows are defined as:

$\begin{align} &\bullet\,\,\, \mathcal P_1=\{1,3,4,5\}\quad &\quad&\bullet\,\,\,\mathcal P_2=\{9,10,7,6\} \\ &\bullet\,\,\, \mathcal P_3=\{2,3,4,7,10,11\}\quad &\quad&\bullet\,\,\,\mathcal P_4=\{2,3,4,7,10,11\} \\ &\bullet\,\,\,\mathcal P_5=\{2,3,4,7,8\}. \end{align}$

And $R_1$ to $R_5$ corresponding to $\tau_1$ to $\tau_5$ are:

$\displaystyle\begin{array}{|c|c|} \hline \tau_1 & \tau_2 & \tau_3 & \tau_4 & \tau_5 \\ \hline 31 & 43 & 53 & 53 & 44 \\ \hline \end{array}$

So how to deduce the results?


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