Preemptive Scheduling with Variable Profile, Precedence Constraints and Due Dates

This paper is concerned with the problem of scheduling preemptive tasks subject to precedence constraints in order to minimize the maximum lateness and the makespan. The number of available parallel processors is allowed to vary in time. It is shown that when an Earliest Due Date rst algorithm provides an optimal nonpreemptive schedule for unit-execution-time (UET) tasks, then the preemptive priority scheduling algorithm, referred to as Smallest Laxity First, provides an optimal preemptive schedule for real-execution-time (RET) tasks. When the objective is to minimize the makespan, we get the same kind of result between Highest Level First schedules solving nonpreemptive tasks with UET and the Longest Remaining Path rst schedule for the corresponding preemptive scheduling problem with RET tasks. These results are applied to four speciic proole scheduling problems and new optimality results are obtained.