Preemptive scheduling of uniform machines subject to release dates : (preprint)

We shall be concerned with finding optimal preemptive schedules on parallel machines, subject to release dates for the jobs. Two polynomial-time algorithms are presented. The first algorithm minimizes maximum completion time on an arbitrary number of uniform machines. The second algorithm minimizes maximum lateness with respect to due dates for the jobs on an arbitrary number of identical machines or on two uniform machines. A third algorithm for minimizing maximum lateness on an arbitrary number of uniform machines is briefly discussed. NP-hardness is established for the problem of minimizing total weighted completion time on a single machine.