A bin packing problem with over-sized items

This paper considers a variable-sized bin packing problem with over-sized items, where some item sizes are larger than the largest size of bins, In practice, two-stage procedures are used to handle this problem. The first stage is to pack each over-sized item into the largest bins fully, and the second stage is to pack the remaining parts of the over-sized items and non-over-sized items using the methods of variable-sized bin packing. We analyze two-stage procedures in a worst case version and find that the procedures have no better worst case ratios than 2. Finally we give an on-line algorithm with an asymptotic worst case ratio no worse than (7)/(4). (C) 2002 Elsevier Science B.V. All rights reserved.