Approximation for preemptive scheduling stochastic jobs on identical parallel machines

In this paper, the stochastic scheduling problem of minimizing the total weighted completion time on preemptive identical parallel machines is investigated. Each job has a processing time, which is a random variable and just given their distribution function. First, we extend the stochastic single-machine preemptive WSEPT rule to a multi-machine list scheduling policy, which we call P-WSEPT. T hen, we use LP based policy to analysis the performance guarantee of preemptive stochastic scheduling with release dates.