A joint optimization-simulation model to minimize the makespan on a repairable machine

We consider the problem of scheduling a set of jobs on a single machine subject to stochastic failures. The objective is to minimizing the makespan. The machine could be stopped for preventive maintenance occasionally to reduce the risk of failure and to improve its reliability. Furthermore, in the case of a breakdown, the machine undergoes a corrective maintenance which brings the age of the machine to zero (That is to say the machine is considered as good as new) and the current processed job is reprocessed from the beginning. Despite the fact that the scheduling problem with single or periodic maintenance has been well studied, most of the studies considered only deterministic cases. In other words the machine never fails. In this paper we take into account the stochastic failures while minimizing the makespan and determining the corresponding optimal sequence of jobs and optimal preventive maintenance policy. Both the exponential and the Weibull distribution are considered to model the probability density function associated with the lifetime of the machine. We use Arena and Optquest to optimize the performance criterion which allows us choosing the best sequence of jobs and the best amount of preventive maintenance.