We consider two-dimensional rectangular strip packing without rotation of items and without the guillotine cutting constraint. We propose a single-pass heuristic which fills every free space in a onedimensional knapsack fashion, i.e. considering only item widths. It appears especially important to assign suitable heuristic "pseudo-values" as profits in this knapsack problem. This simple heuristic improves the results for most of the test classes from the literature, compared to the results of Bortfeldt (2004) and . Moreover, we describe a simple modification of the Bottom-Left heuristic and call it Bottom-Left-Right. Executing it iteratively with different input sequences generated by the randomized framework BubbleSearch of , we obtain the best results in some classes with smaller number of items (20, 40). For larger instances, the pseudo-value-based algorithm is the best one in most cases.
Two algorithms for the one-dimensional cutting problem, namely, a modified branch-and-bound method (exact method) and a heuristic sequential value correction method are suggested. In order to obtain a reliable assessment of the efficiency of the algorithms, hard instances of the problem were considered and from the computational experiment it seems that the efficiency of the heuristic method appears to be superior to that of the exact one, taking into account the computing time of the latter. A detailed description of the two methods is given along with suggestions for their improvements.
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