Stochastic Online Scheduling with Precedence Constraints

We consider the preemptive and non-preemptive problems of scheduling jobs with precedence constraints on parallel machines with the objective to minimize the sum of (weighted) completion times. We investigate an online model in which the scheduler learns about a job when all its predecessors have completed. For scheduling on a single machine, we show matching lower and upper bounds of Θ(n) and Θ( √ n) for jobs with general and equal weights, respectively. We also derive corresponding results on parallel machines. Our result for arbitrary job weights holds even in the more general stochastic online scheduling model where, in addition to the limited information about the job set, processing times are uncertain. For a large class of processing time distributions, we derive also an improved performance guarantee if weights are equal.