We consider dynamic stochastic scheduling of preemptive jobs with processing times that follow independent discrete probability distributions. We derive a policy with a guaranteed performance ratio of 2 for the problem of minimizing the sum of weighted completion times on identical parallel machines subject to release dates. The analysis is tight. Our policy as well as their analysis applies also to the more general model of stochastic online scheduling.In contrast to previous results for nonpreemptive stochastic scheduling, our preemptive policy yields an approximation guarantee that is independent of the processing time distributions. However, our policy extensively utilizes information on the distributions other than the first (and second) moments. We also introduce a new nontrivial lower bound on the expected value of an unknown optimal policy. It relies on a relaxation to the basic problem on a single machine without release dates, which is known to be solved optimally by the Gittins index priority rule. This dynamic priority index is crucial to the analysis and also inspires the design of our policy.Keywords: scheduling; stochastic; approximation algorithm; total weighted completion time MSC2000 subject classification: Primary: 90B36; secondary: 68W40 OR/MS subject classification: Primary: production/scheduling; secondary: approximation/heuristic History: Received August 15, 2011; revised March 9, 2014. Published online in Articles in Advance.1. Introduction. Stochastic scheduling problems have attracted researchers for about four decades. A full range of articles is concerned with criteria that guarantee the optimality of simple policies for special scheduling problems; see, e.g., Pinedo [26]. It is only recently that research also focuses on approximations for less restrictive problem settings (Möhring et al. All these results apply to nonpreemptive scheduling, and we are not aware of any approximation results when job preemption is allowed and processing times are stochastic.In this paper, we give the first constant factor approximation for the stochastic version of the classical problem of scheduling jobs preemptively, with or without release dates, on identical parallel machines. The objective is to minimize the expected sum of weighted completion times.We provide a very natural scheduling policy and show that it has an expected objective value of at most twice the expected optimal value. The analysis of our policy is tight. Both, the policy and its analysis are also valid in the model of stochastic online scheduling (Megow et al. [19], Chou et al. [5], Vredeveld [39]). They rely on the celebrated Gittins index priority rule (Gittins [9, 10]), which is an optimal policy for the setting when there is only one machine and there are no nontrivial release dates (Sevcik [33], Weiss [41]). Under deterministic input, our policy corresponds to the preemptive weighted shortest processing time (WSPT) rule, which is known to have a tight performance guarantee of 2 on identical parallel machines (Megow and Schulz...