Single machine scheduling with random processing time

The sequencing of n independent work pieces which are processed in a single-machine shop is discussed in which each job is assigned a common due-date k and each work piece processing time distribution is assumed to be independent normal distribution. The object is to determine a common due-date k* and to find an optimal sequence of n independent workpieces to minimise the expectation of the linear combination of total absolute deviation of completion time about a common due date and total completion time.