In this paper, we consider the two-dimensional rectangular strip packing problem, in the case where there is a perfect packing; that is, there is no wasted space. One can think of the problem as a jigsaw puzzle with oriented rectangular pieces. Although this comprises a quite special case for strip packing, we have found it useful as a subroutine in related work. We demonstrate a simple pruning...

We consider the relaxed online strip packing problem, where rectangular items arrive online and have to be packed into a strip of fixed width such that the packing height is minimized. Thereby, repacking of previously packed items is allowed. The amount of repacking is measured by the migration factor, defined as the total size of repacked items divided by the size of the arriving item. First, ...

Here, we focus on a generalized version of the strip packing problem; namely have several open-end strips with different widths, and wish to pack rectangular items into these without overlapping such that minimize either makespan (i.e. top topmost item), or total area used. We investigate online variant problem, where are arriving one-by-one, make irrevocable decisions their packing. A similar ...

The two-dimensional level strip packing problem (2LSPP) consists in packing rectangular items of given size into a strip of given width divided into levels. Items packed into the same level cannot be put on top of one another and their overall width cannot exceed the width of the strip. The objective is to accommodate all the items while minimizing the overall height of the strip. The problem i...

In [J. Csirik, G.J. Woeginger, An on-line algorithm for multidimensional bin packing, Inform. Process. Lett. 63 (1997) 171–175] the authors study the asymptotic worst case ratio between the height of the strip needed to on-line pack a list of boxes by means of the Harmonic Shelf Algorithm and the height of the strip used by an optimal algorithm. In this note we analyze the effectiveness of the ...

This paper presents a packing algorithm to solve an irregular shape strip packing problem. The polygons are packed in strip material, which limits a bin width but not limits a bin length. The objective of a packing algorithm is to minimize a bin length. This paper proposes a hybrid method of genetic algorithms and tabu search to solve a packing problem. Initially, a hybrid method behaves like r...

We present an asymptotic fully polynomial approximation scheme for strip-packing, or packing rectangles into a rectangle of xed width and minimum height, a classical N P-hard cutting-stock problem. The algorithm nds a packing of n rectangles whose total height is within a factor of (1 +) of optimal (up to an additive term), and has running time polynomial both in n and in 1==. It is based on a ...

We present an qpproximation scheme for strip-packing, or packing rectangles into a rectangle of fixed width and minimum height, a classical NP-hard cutting-stock problem. The algorithm find,!; a packing of n rectangles whose total height is within a ,factor of (1 + E ) of optimal, and has running time polynomial both in n and in 1 / E . It is based on a reduction to fractional bin-packing, and ...

We investigate the best-fit heuristic algorithm by Burke et al. [Operations Research 52 (2004) 655–671] for the rectangular strip packing problem. For its simplicity and good performance, the best-fit heuristic has become one of the most significant algorithms for the rectangular strip packing. In this paper, we propose an efficient implementation of the best-fit heuristic that requires linear ...