Single machine scheduling when processing times are correlated normal random variables

A single machine is available to process a collection of jobs whose processing times are jointly multivariate normal. Processing is nonpreemptive. We show that in the equicorrelation case, the permutational policy which schedules the jobs in ascending order of their (marginal) mean processing times is optimal for general order-specific costs and also for job-specific costs under an agreeability condition. Suboptimality bounds on the performance of Smith's rule are obtained for the weighted flow-time criterion. A computational study shows that a dynamic version of Smith's rule comes very close to optimality.