Abstract.
The bin packing problem is one of the classical NP-hard optimization problems. In this paper, we present a simple generic approach for obtaining new fast lower bounds, based on dual feasible functions. Worst-case analysis as well as computational results show that one of our classes clearly outperforms the previous best “economical” lower bound for the bin packing problem by Martello and Toth, which can be understood as a special case. In particular, we prove an asymptotic worst-case performance of 3/4 for a bound that can be computed in linear time for items sorted by size. In addition, our approach provides a general framework for establishing new bounds.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: August 11, 1998 / Accepted: February 1, 2001¶Published online September 17, 2001
Rights and permissions
About this article
Cite this article
Fekete, S., Schepers, J. New classes of fast lower bounds for bin packing problems. Math. Program. 91, 11–31 (2001). https://doi.org/10.1007/s101070100243
Issue Date:
DOI: https://doi.org/10.1007/s101070100243