A probabilistic analysis of the dual bin packing problem

In the dual bin packing problem, the objective is to assign items of given size to the largest possible number of bins, subject to the constraint that the total size of the items assigned to any bin is at least equal to 1. We carry out a probabilistic analysis of this problem under the assumption that the items are drawn independently from the uniform distribution on [0,1], and reveal the connections between this problem and the classical bin packing problem as well as to renewal theory.