\[ \max \sum_{g=1}^G \sum_{t=1}^{BT} \sum_{r=1}^{R_t} x_{gtr} \cdot n_g \cdot p_i \]
\[ \sum_{t=1}^{BT} \sum_{r=1}^{R_t} x_{gtr} = 1, \quad \forall g \]
\[\begin{eqnarray} a_{tr} &\ge& x_{gtr}, \quad \forall t \in \{1,2,\ldots,BT \},\;r \\ a_{tr} &\le& \sum_{g=1}^G x_{gtr}, \quad \forall t \in \{1,2,\ldots,BT \},\;r \\ a_{tr} &\ge& r_{min}, \quad \forall t \in \{1,2,\ldots,T \} \end{eqnarray}\]
\[ \sum_{r=1}^{R} a_{tr} = \sum_{r=1}^R a_{(bT+t)r}, \quad \forall t \in \{1,2,\ldots,T \},\; \min(1,B-1)\le b \le \max(0, B-1) \] ## Number of students per subgroup
\[\begin{eqnarray} \sum_{i=1}^N \sum_{g=1}^G m_{ig} \cdot x_{gtr} &\ge& a_{tr} \cdot n_{tr}^{min}, \quad \forall t \in \{1,2,\ldots,BT \},\;r \\ \sum_{i=1}^N \sum_{g=1}^G m_{ig} \cdot x_{gtr} &\le& a_{tr} \cdot n_{tr}^{max}, \quad \forall t \in \{1,2,\ldots,BT \},\;r \end{eqnarray}\]
\[\begin{eqnarray} x_{gtr} &\in& \{0,1\} \\ a_{tr} &\in& \{0,1\} \end{eqnarray}\]