Job sequencing using an expert

We study the benefits of using an expert's estimates of unknown service times to order a batch of jobs of fixed size prior to machine processing. Although the estimates may be incorrect, the jobs are reordered based on the estimates to reduce the sum of the flow times of all jobs in the batch. We examine a system with two job times and obtain closed analytical results for the expectation of total flow time. Furthermore, we analyze the amount by which the expert's ordering is better than random processing order, and how the expert's accuracy affects these results.