An analysis of lower bound procedures for the bin packing problem

In this paper, we review LB2 and LB3, two lower bounds for the bin packing problem that were respectively introduced by Martello and Toth by Labbé, Laporte and Mercur. We prove that LB3⩾LB2. We also prove that the worse-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.