Tight Bounds for an Online Bin Packing Problem

The following online bin packing problem is considered: Items with integer sizes are given and variable sized bins arrive online. A bin must be used if there is still an item remaining which fits in it when the bin arrives. The goal is to minimize the total size of all the bins used. Previously, a lower bound of 5 4 on the competitive ratio of this problem was achieved using jobs of size S and 2S−1 and maximum bin size 4S−4. For this case, we obtain matching upper and lower bounds, which vary depending on the ratio of the number of small jobs to the number of large jobs.