for an appearance of all large and medium jobs in patterns while (3) will ensure every small job will be placed somewhere. The constraint (4) will ensure that the average area that is scheduled on top of a pattern does not exceed the optimal height $T$. To respect conflicts among priority bags we added constraint (5). Constraint (5) first will not allow to pack any small job of a bag $B_l$ on top of a pattern $p$ that already holds large or medium jobs of $B_l$. Additionally this constraint will also only allow to place at most as many jobs of one bag $B_l$ on top of a pattern $p$ as the amount of machines the pattern was assigned to. This will help us later on when placing small jobs and will prevent conflicts between small jobs itself.

The variable constraints ensure that all $x$ variables are integral and most of the $y$ variables are fractional. The only exception are $y_p^{B_l^s}$ variables that belong to a priority bag $B_l$ with $l\in A$ and have an item size $s> \epsilon^{2k+11}$. We make sure that items of this size are packed as full jobs, as we are later going to round the 