these entries are the bags and the size of the slot, we merely use $B_l^s$ as a notation for these entries instead of the pair $(l,s)$.

In our MILP we use integer variables $x_p$ for all patterns $p\in \mathscr{P}$. $x_p$ indicates how many machines will hold patterns of the form $p$. To consider a placement of small jobs for later we introduce variables of the form $y_p^{B_l^s}$ for any bag $B_l$ and any small item size $s$. These variables indicate how many jobs of $B_l^s$ we are going to place on top of a pattern $p$. A majority of these variables are going to be fractional but a constant number of $y$ variables will be integral, to ensure we can pack these jobs later without increasing the makespan by too much. In the MILP we will also make sure that the number of jobs and the assigned area to a pattern may not grow too large.

To formally define the MILP we are going to introduce some additional notations. First of all let $A$ be set of all indices of priority bags such that $l\in A$ means that $B_l$ is a priority bag and set $S_{small}$ to be the set 