Stochastic single machine scheduling with random common due date

This paper studies the single machine scheduling problem for minimising the expected total weighted deviations of completion times from random common due date. Jobs have exponentially distributed processing times and the common due date is a generalised Erlang distribution. The optimal schedules are shown to be boolean AND-shaped. Moreover, we give the optimal schedules when the machine is subject to stochastic breakdowns with independent and exponentially distributed uptimes and downtimes.