Online bin stretching with three bins

Online Bin Stretching is a semi-online variant of bin packing in which the algorithm has to use the same number of bins as an optimal packing, but is allowed to slightly overpack the bins. The goal is to minimize the amount of overpacking, i.e., the maximum size packed into any bin. We give an algorithm for Online Bin Stretching with a stretching factor of 11/8 = 1.375 for three bins. Additionally, we present a lower bound of 45/33 = 1.36 for Online Bin Stretching on three bins and a lower bound of 19/14 for four and five bins that were discovered using a computer search.