Stochastic Online Scheduling Revisited

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We consider the problem of minimizing the total weighted completion time on identical parallel machines when jobs have stochastic processing times and may arrive over time. We give randomized as well as deterministic online and off-line algorithms that have the best known performance guarantees in either setting, deterministic and off-line or randomized and online. Our analysis is based on a novel linear programming relaxation for stochastic scheduling problems, which can be solved online.