On stochastic machine scheduling with general distributional assumptions

A set of stochastic jobs is to be processed on a single machine which is subject to breakdowns and repairs. Under quite general conditions on the job's processing times, the uptimes and the repair times of the machine, we find a simple optimal permutation policy for the weighted sum of an increasing function of the completion times. Some optimal policies for two special cases, which have not been investigated in the literature, are given. Moreover, an upper bound is established on the loss incurred when a processing policy is adopted under a simplifying assumption of exponential processing requirements.