Heuristics for the container loading problem

The knapsack container loading problem is the problem of loading a subset of rectangular boxes into a rectangular container of fixed dimensions such that the volume of the packed boxes is maximized. A new heuristic based on the wall-building approach is proposed, which decomposes the problem into a number of layers which again are split into a number of strips. The packing of a strip may be formulated and solved optimally as a Knapsack Problem with capacity equal to the width or height of the container. The depth of a layer as well as the thickness of each strip is decided through a branch-and-bound approach where at each node only a subset of branches is explored. Several ranking rules for the selection of the most promising layer depths and strip widths are presented and the performance of the corresponding algorithms is experimentally compared for homogeneous and heterogeneous instances. The best ranking rule is then used in a comprehensive computational study involving large-sized instances. These computational results show that instances with a total box volume up to 90% easily may be solved to optimality, and that average fillings of the container volume exceeding 95% may be obtained for large-sized instances.