T. Buchwald and G. Scheithauer
Upper Bounds for Heuristic Approaches to the Strip Packing Problem
We consider the two- and three-dimensional strip packing problem (SPP): given a set of rectangular items and a strip, find the minimal height needed to pack all items. Rotation of the items is not permitted. We present an algorithm for the two-dimensional SPP, which improves the packing of the well-known FFDH-heuristic and state theoretical results of this algorithm. Furthermore, we prove new upper bounds for the three-dimensional SPP in special cases. Moreover, we present an implementation of the FFDH-heuristic for the three-dimensional case, which is used to construct a new algorithm with known performance guaranty. Based on the new algorithm, we also prove a general upper bound depending on the continuous lower bound and the maximum height lower bound and show that the combination of both lower bounds has an absolute worst case performance ratio of at most 5.
PDF, (Preprint MATH-NM-05-2013, TU Dresden, June 2013)