Polynomial algorithms for resource-constrained and multiprocessor task scheduling problems

Resource-constrained scheduling problems with a fixed number of task types are considered in which, in addition, either the processing times are bounded or the number of processors is fixed. For problems with makespan, (weighted) mean now time, weighted number of tardy tasks, and sum of tardiness as objective functions polynomial time algorithms are presented. These algorithms generalize results derived by Blaiewicz ct al. (1989) for makespan problems and solve open problems listed by Hoogeveen et al. (1994). Furthermore, results for shop problems with multiprocessor tasks and unit processing times, in which either the number of jobs or the number of stages is fixed, are derived.