The authors consider sequencing n jobs on a single machine subject to job completion times arising from either machine breakdowns or other causes. The objective is to minimize an expected weighted combination of due dates, completion times, earliness, and tardiness penalties. The determination of optimal distinct due dates or optimal common due dates for a given schedule is investigated. The scheduling problem for a fixed common due date is considered when random completion times arise from machine breakdowns. The optimality of a v-shaped about (a point) T sequence is established when the number of machine breakdowns follows either a Poisson or a geometric distribution and the duration of a breakdown has an exponential distribution.
