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.