On-Line Bin Packing with Arbitrary Release Times

We study a new variant of on-line bin packing problem, in which each item ai is associated with a size ai and also a release time ri so that it must be placed at least ri above from the bottom of a bin. Items arrive in turn and must be assigned without any knowledge of subsequence items. The goal is to pack all items into unit-size bins using the minimum number of bins. We study the problem with all items have equal size. First, we show that the ANY FIT algorithm cannot be approximated within any constant. Then we present a best possible on-line algorithm with asymptotic competitive ratio of 2.