New Classes of Lower Bounds for Bin Packing Problems

The bin packing problem is one of the classical NP-hard optimization problems. Even though there are many excellent theoretical results, including polynomial approximation schemes, there is still a lack of methods that are able to solve practical instances optimally. In this paper, we present a fast and simple generic approach for obtaining new lower bounds, based on dual feasible functions. Worst case analysis as well as computational results show that one of our classes clearly outperforms the currently best known "economical" lower bound for the bin packing problem by Martello and Toth, which can be understood as a special case. This indicates the usefulness of our results in a branch and bound framework.