Column-Based Strip Packing Using Ordered and Compliant Containment

The oriented strip packing problem is very important to manufacturing industries: given a strip of xed width and a set of many (> 100) nonconvex polygons with 1, 2, 4, or 8 orientations permitted for each polygon, nd a set of translations and orientations for the polygons that places them without overlapping into the strip of minimum length. Heuristics are given for two versions of strip packing: 1) translation-only and 2) oriented. The rst heuristic uses an algorithm we have previously developed for translational containment: given polygons P1; P2; : : : ; P k and a xed container C , nd translations for the polygons that place them into C without overlapping. The containment algorithm is practical for k 10. Two new containment algorithms are presented for use in the second packing heuristic. The rst, an ordered containment algorithm , solves containment in time which is only linear in k when the polygons are a) \long" with respect to one dimension of the container and b) ordered with respect to the other dimension. The second algo-that allows all l + k polygons to t into the container without overlapping. The performance of the heuristics is compared to the performance of commercial software and/or human experts. The results demonstrate that fast containment algorithms for modest values of k (k 10) are very useful in the development of heuristics for oriented strip packing of many (k >> 10) polygons.