no original bag of the instance. With these notations we can now construct our MILP.

$$\begin{aligned}
{3}
 && \sum\limits_{p \in \mathscr{P}}{x_p} \le m \quad & \\
&&\sum\limits_{p \in \mathscr{P}}{(x_p *\chi_p(B_l^{s}))} \ge |B_l^{s}| \quad&  \forall s \in S_{ml}, l \in A \cup \{x\}\\
&&\sum\limits_{p \in \mathscr{P}}{y^{B_l^{s}}_p} \ge |B_l^{s}| \quad&  \forall s \in S_{small}, l \le b\\
&&\sum\limits_{s \in S_{small}, l \le b}{y^{B_l^{s}}_p} *s \le x_p * (T- height(p)) \quad&  \forall p \in \mathscr{P}\\
&&\sum\limits_{s_i \in S_{small}}{y^{B_l^{s_i}}_p}  \le x_p * (1 - \chi_p(B_l)) \quad&  \forall p \in \mathscr{P}, l \le b\\
&& x_p \in \mathbb{N}_{\ge 0} \quad&  \forall p \in \mathscr{P} \\
&& y_p^{B_l^s} \in \mathbb{N}_{\ge 0} \quad&  \forall p \in \mathscr{P}, s\in S_{small},  s> \epsilon^{2k+11}, l \in A \\
&& y_p^{B_l^s} \in \mathbb{R}_{\ge 0} \quad&  \forall p \in \mathscr{P}, s\in S_{small},  s \le  \epsilon^{2k+11}, l\in A \\
&& y_p^{B_l^s} \in \mathbb{R}_{\ge 0} \quad&  \forall p \in \mathscr{P}, s\in S_{small},  l\le b, l \not \in A\end{aligned}$$

The first condition of our MILP will ensure that we consider at most $m$ patterns as we only have $m$ machines to fill. Conditions (2) and (3) take care that every job of our instance will be placed on some machine. Constraint (2) will specifically check 