The problem addressed in this paper is that of orthogonally packing a given set of rectangular-shaped boxes into the minimum number of rectangular bins. The problem is strongly NP-hard and extremely diicult to solve in practice. Lower bounds are discussed, and it is proved that the asymptotical worst-case performance of the continuous lower bound is 1 8. An exact algorithm for lling a single bin is developed, leading to the deenition of an exact branch-and-bound algorithm for the three-dimensional bin packing problem, which also incorporates original approximation algorithms. Extensive computational results, involving instances with up to 60 boxes, are presented: it is shown that many instances can be solved to optimality within a reasonable time limit.
translated by 谷歌翻译