We study a new kind of on-line bin packing motivated by a problem arising when scheduling jobs on the Grid. In this bin packing problem, the set of items is given at the beginning, and variable-sized bins arrive one by one. A closely related problem was introduced by Zhang in 1997. Our main result answers a question posed in that paper in the affirmative: we give an algorithm with a competitive ratio strictly better than 2, for our problem as well as Zhang's problem.
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