A Lower Bound for the Non-Orineted Two-Dimensionl Bin Packing Problem

Given a set of rectangular items, and an unlimited number of identical rectangular bins, we consider the problem of allocating, without overlapping, all the items to the minimum number of bins. We assume that the items may be rotated by 90◦. The problem is strongly NP-hard, and has several industrial applications. No specific lower bound is known for it. We present a lower boundwhich explicitly takes into account the possible item rotation. The bound is embedded into an exact branch-and-bound algorithm. The average performance is evaluated through computationalexperiments.