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It sounds like you want to pack $N$ rectangles with given dimensions $w_i \times h_i$ in a $W \times H$ rectangle, as discussed here. To allow each rectangle to be rotated 90 degrees (with dimensions $h_i \times w_i$), you can introduce a binary variable $r_i$ to indicate whether to rotate rectangle $i$ or not. Then modify the constraints like this: \begin{...

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