Packing of convex polytopes into a parallelepiped

Authors: Y. Stoyan, N. Gil, G. Scheithauer, A. Pankratov, I.Magdalina

Preprint MATH-NM-04-2003, TU Dresden, April 2003.
Appeared in Optimization 54/2 (2005) 215-236

This paper 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 a method to compute local optimal solutions is constructed. Both an approximate and an exact method to search for local minima of the problem are discussed. The exact method is a special modification of the duel simplex method. Some examples are also given.

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