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.