Simple but effective heuristics for the 2-constraint bin packing problem

The 2-constraint bin packing problem consists in packing a given number of items, each one characterised by two different but not related dimensions, into the minimum number of bins in such a way to do not exceed the capacity of the bins in either dimension. The development of the heuristics for this problem is challenged by the need of a proper definition of the criterion for evaluating the feasibility of the two capacity constraints on the two different dimensions. In this paper, we propose a computational evaluation of several criteria, and two simple but effective algorithms—a greedy and neighbourhood search algorithms—for solving the 2-constraint bin packing problem. An extensive computational analysis supports our main claim.