Abstract
A single machine scheduling problem for jobs with stochastic processing time is considered in this study. Shortest processing time (SPT) sequencing according to the expected processing times of jobs is optimal for schedules with minimal expected mean flow time when all the jobs arrive to be scheduled and their expected processing times are known. However, SPT sequencing according to the expected processing time may not be optimal for the minimization of the mean flow time when the actual processing times of jobs are known. This study evaluates the complexity of SPT sequencing through a comparison of the mean flow times of schedules based on the expected processing times and actual processing times of randomly generated jobs. Evaluation results show that SPT sequencing according to the expected flow time exhibits chaotic variation to the optimal mean flow time. The relative deviation from the optimal mean flow time increases as the number of jobs, processing time, or coefficient of variation increases.
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