| Article ID: | iaor2013662 |
| Volume: | 7 |
| Issue: | 2 |
| Start Page Number: | 375 |
| End Page Number: | 405 |
| Publication Date: | Feb 2013 |
| Journal: | Optimization Letters |
| Authors: | Andrade R, Birgin E |
| Keywords: | combinatorial optimization |
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.