Scheduling Stochastic jobs on a repairable machine with general phase type uptime

A set of jobs, with stochastic processing times, is to be processed on a machine which is subject to breakdown and repair. The machine’s uptime is assumed to have a general phase type distribution, the processing time of each job and the repair times of the machine are generally considered as arbitrary random variables. Simple permutation policies depending on both machine parameters and jobs processsing distributions are derived to minimize in expectation of the weighted flow times, the weighted number of tardy jobs and the weighted sum of the job delays. Some simple optimal schedules for uptimes with hyper-exponential distribution and Erlang distribution are deduced from the general results. Copyright Springer-Verlag 2005