A joint maintenance and production strategy to minimize the makespan

In this paper, we study the problem of scheduling n jobs without preemption on a machine subject to random failures. To illustrate the performance of the proposed strategy, we consider the production sequence as non-fixed. The machine undergoes minimal repair whenever it fails. To minimize the makespan (C_max), that is to say, the total length of the schedule, a joint management of the production and preventive maintenance is implemented. This joint management approach improves the makespan, which is considered as a production performance. The proposed strategy consists in the determination of the probabilistic moments of the next failure given the age of the machine. To minimize makespan, preventive maintenance actions are performed regularly on the machine to ensure that its reliability is always greater than or equal to a minimum value R_min. A simulation model has been developed for this strategy. It takes into account the probability distributions associated with the lifetime of the machine, the periodicity of the preventive maintenance and the processing time of the jobs. A numerical example is given to illustrate the effectiveness of the proposed strategy.