In this paper, we investigate fast lower bounds for the deterministic one-dimensional bin packing problem. We present two variants of a general lifting procedure which aims at systematically tightening a given lower bound. We describe several enhancements which improve the efficiency of the proposed procedure. Extensive numerical experiments show that the proposed lifting procedures consistently improve lower bounds from the literature.

We address a generalization of the classical multiprocessor scheduling problem with non simultaneous machine availability times, release dates, and delivery times. We develop new lower and upper bounds as well as a branching strategy which is based on a representation of a schedule as a permutation of jobs. We show that embedding a semi-preemptive lower bound based on max-flow computations in a branch-and-bound algorithm yields very promising performance.

In this paper, we investigate new lower bounds for the P|rj,qj|Cmax scheduling problem. A new bin packing based lower bound, as well as several new lifting procedures are derived for this strongly NP -hard problem. Extensive numerical experiments show that the proposed lower bounds consistently outperform the best existing ones.