An analysis of lower bound procedures for the bin packing problem

Authors:
Jean-Marie Bourjolly;Vianney Rebetez
Affiliations:
Centre de Recherche Sur les Transports, Université de Montréal, and Département de Management et Technologie, Université du Québec à Montréal, C.P. 8888, Succ. C ...;Service de Mathématiques de la Gestion, Université Libre de Bruxelles, Campus de la Plaine CP 210/01, Boulevard du Triomphe, B-1050 Bruxelles, Belgium
Venue:
Computers and Operations Research
Year:
2005

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Abstract

In this paper, we review LB2 and LB3, two lower bounds for the bin packing problem that were respectively introduced by Martello and Toth and by Labbé, Laporte and Mercure. We prove that LB3 ≥ LB2. We also prove that the worst-case asymptotic performance ratio of LB3 is 3/4 and that this ratio cannot be improved. We study LB2, LB3 and three of their variants both analytically and computationally. In particular, we clarify the relationships between LB2", the bound implemented by Martello and Toth in their well-known bin packing code, and both LB2 and LB3.