Upper bounds and algorithms for the maximum cardinality bin packing problem

In the maximum cardinality bin packing problem, we are given m bins of capacity c and n items of weight wi(i=1,…,n). The objective is to maximize the number of items packed into the m bins without exceeding bin capacities and without splitting items. Several upper bounds are derived. These are then embedded in an enumeration algorithm. Computational results indicate that the algorithm typically identifies an optimal solution within very low computing times.