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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 54, 2005 - Issue 2
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Original Articles

Packing of convex polytopes into a parallelepiped

Y. G. Stoyan Institute of Problems in Machinery, National Academy of Science, Kharkov, Ukraina
,
N. I. Gil Institute of Problems in Machinery, National Academy of Science, Kharkov, Ukraina
,
G. Scheithauer Institute for Numerical Mathematics, Dresden University of Technology, D-01062 Dresden, GermanyCorrespondence[email protected]
,
A. Pankratov Institute of Problems in Machinery, National Academy of Science, Kharkov, Ukraina
&
I. Magdalina Institute of Problems in Machinery, National Academy of Science, Kharkov, Ukraina
Pages 215-235 | Received 07 Jan 2004, Accepted 03 Dec 2004, Published online: 20 Aug 2006
 
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Abstract

This article deals with the problem of packing convex polytopes into a parallelepiped of minimal height. It is assumed that the polytopes are oriented, i.e. rotations are not permitted. A mathematical model of the problem is developed and peculiarities of them are addressed. Based on these peculiarities an exact method to compute local optimal solutions is constructed. This method uses a special modification of the Simplex method. Some examples are also given.

Acknowledgement

The authors wish to thank the anonymous referee for her/his valuable remarks and hints which helped a lot to improve the presentation. This work was partially supported by the German Research Society (DFG, grant TE 207/7, 436 UKR 113/42/0).

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