Packing batches of items into a single bin

Abstract In λ-packing items are grouped in batches. Items arrive one by one (online) and they are stored in a buffer until either the total volume of stored items is greater than or equal to λ or all items have already arrived. Then items from the buffer are packed offline into a unit capacity bin and the buffer is emptied. We show that any sequence of squares with total area not greater than 1/2 can be 1/4-packed into a single bin (a unit square).