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I have a problem where I need to find the combination of boxes. Let say I have 3 small boxes with different sizes and I need to fit all these boxes into different size trucks but at the same time, I will need to minimize the truck cost. I tried the linear programming solution but it is not optimal in the sense, the solution does not cover that the length, width, and height of the boxes are also important.

For example, I cant fit a 2 x 2 x 2 item in a 1 x 15 x 1 box. Is there any insight on how to add this constraint to my LP?

Please advise.

chandra sutrisno
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  • The example can just be tackled by some element-wise inequality over some n-dim vector: `(item_dim1, item_dim2, item_dim3` <= `box_dim1, box_dim_2, box_dim3`. But that's probably not helping much as those problems usually get interesting when it's about *placements* of multiple items side-by-side.Maybe do some research with the keywords *3d-packing* or *multidimensional packing* and try to ask a more explicit question after analyzing those ideas.I guess there are easier things to tackle with integer-progr than this one...I wouldn't be surprised to see lots of (meta-)heuristics used in practice – sascha Nov 11 '21 at 11:12

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This is 3D Bin Packing algo. I have solved this.

chandra sutrisno
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