On-line sequential bin packing.
We consider a sequential version of the classical bin packing problem in which items are received one by one. Before the size of the next item is revealed, the decision maker needs to decide whether the next item is packed in the currently open bin or the bin is closed and a new bin is opened. If the new item does not fit, it is lost. If a bin is closed, the remaining free space in the bin accounts for a loss. The goal of the decision maker is to minimize the loss accumulated over n periods. We present an algorithm that has a cumulative loss not much larger than any strategy in a finite class of reference strategies for any sequence of items. Special attention is payed to reference strategies that use a fixed threshold at each step to decide whether a new bin is opened. Some positive and negative results are presented for this case.