Preemptive weighted completion time scheduling of parallel jobs

We present a new algorithm for the preemptive offline scheduling of independent jobs on a system consisting of m identical machines. The jobs can be parallel; that is, they may need the concurrent availability of several machines for their execution. To this end, we introduce a machine model which is based on existing multiprocessors and accounts for the penalty of preemption. After examining the relation between makespan and total weighted completion time costs for the scheduling of parallel jobs, we show that our new algorithm achieves an approximation factor of 2.37 for total weighted completion time scheduling if no preemption penalty is considered. This compares favorably to the thus far best approximation factor of 8.53 for the nonpreemptive case. To fine-tune the algorithm with respect to different preemption penalties, we use a fairly simple numerical optimization problem. Further, we present an algorithm to transform the preemptive schedule into a nonpreemptive one. This leads to an improved approximation factor of 7.11 for the nonpreemptive weighted completion time scheduling.