In this paper we consider a production process at operative level on m identical parallel machines, which are subject to stochastic machine failures. To avoid long downtime of the machines, caused by unexpected failures, preventive maintenance activities are planned and conducted, but if a failure could not be averted a corrective maintenance has to be performed. Both maintenance activities are assumed to restore the machine to be Ã¢ÂÂas good as newÃ¢ÂÂ. The maintenance activities, the number of jobs and their allocation to machines as well as their sequence have a large impact on the performance of the production process and the delivery dates. We study an order of n jobs, scheduled for a frozen period on the machines. It is assumed that jobs, interrupted by machine failure, have to get repeated right after the corrective maintenance is finished (non-resumable case). We first derive an exact formula for the expected makespan. Since the exact evaluation of a schedule is highly complex, we propose two approximations for the expected makespan. The excellent performance of the approximations is illustrated in a numerical study. 
Evaluation of the expected makespan of a set of non-resumable jobs on parallel machines with stochastic failures