\(\large
(\text{SSP})~~\left\{~~
\begin{align*}
& \text{Min.} && \rlap{f(x, y, z)=\sum_{t=1}^T(T-t+1)\cdot x_t-\sum_{t=1}^T(T-t)\cdot y_t-d_{br}\sum_{t=1}^T z_t} \\
& \text{u. d. N.} && y_t=0 && (t=1, \ldots, d_{min}-1) \\
& && x_t=0 && (t=T-d_{min}+2, \ldots, T) \\
& && \sum_{t'=1}^t x_{t'}-\sum_{t'=1}^{t-1}y_{t'}-\sum_{t'=\max\{1, t-d_{br}+1\}}^t z_{t'}\ge r_t && (t=1, \ldots, T)\\
& && \sum_{t'=1}^t y_{t'}\le \sum_{t'=1}^{t-d_{min}+1}x_{t'} && (t=d_{min}, \ldots, T)\\
& && \sum_{t'=1}^{t+d_{max}-1}y_{t'} \ge \sum_{t'=1}^t x_{t'} && (t=1, \ldots, T-d_{max}+1)\\
& && \sum_{t=1}^T y_t = \sum_{t=1}^T x_t\\
& && \sum_{t'=1}^t z_{t'}\le \sum_{t'=1}^t x_{t'} && (t=1, \ldots, T)\\
& && \sum_{t'=1}^{t-d_{br}+1} z_{t'}\ge \sum_{t'=1}^t y_{t'} && (t=d_{br}, \ldots, T)\\
& && \sum_{t'=1}^T z_{t'}=\sum_{t'=1}^T x_{t'} \\
& && x_t,~y_t,~z_t\in{}\mathbb{Z}_{\ge 0} && (t=1, \ldots, T)
\end{align*}\right.
\)
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