Abstract
Two problems related to packing identical rectangles within a polyhedron are tackled in the present work. Rectangles are allowed to differ only by horizontal or vertical translations and possibly 90° rotations. The first considered problem consists in packing as many identical rectangles as possible within a given polyhedron, while the second problem consists in finding the smallest polyhedron of a given type that accommodates a fixed number of identical rectangles. Both problems are modeled as mixed integer programming problems. Symmetry-breaking constraints that facilitate the solution of the MIP models are introduced. Numerical results are presented.
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Andrade, R., Birgin, E.G. Symmetry-breaking constraints for packing identical rectangles within polyhedra. Optim Lett 7, 375–405 (2013). https://doi.org/10.1007/s11590-011-0425-9
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DOI: https://doi.org/10.1007/s11590-011-0425-9