Single machine scheduling when processing times are correlated normal random variables

• Published in: European journal of operational research Vol. 102; no. 1; pp. 111 - 123
• Main Authors: Boys, R.J., Glazebrook, K.D., McCrone, C.M.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.10.1997; Elsevier; Elsevier Sequoia S.A
• Series: European Journal of Operational Research
• Subjects: Agreeability; Applied sciences; Dependent processing times; Exact sciences and technology; Job shops; Multivariate analysis; Multivariate normal distribution; Operational research and scientific management; Operational research. Management science; Operations research; Optimal policy; Optimization; Random variables; Scheduling; Scheduling, sequencing; Smith's rule; Stochastic models; Stochastic scheduling; Studies; Smith's rule; Stochastic scheduling; Multivariate normal distribution; Agreeability; Dependent processing times; Optimal policy; Gaussian distribution; Multivariate distribution; Processing time; Scheduling; Covariance matrix; Stochastic process; Random variable; Single machine
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/S0377-2217(96)00211-1

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 permutation 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.