Optimal maintenance policies for serial, multi-machine systems with non-instantaneous repairs

We study optimal age-replacement policies for machines in series with non-instantaneous repair times by formulating two nonlinear programs: one that minimizes total cost-rate subject to a steady-state throughput requirement and another that maximizes steady-state throughput subject to a cost-rate budget constraint. Under reasonable assumptions, the single-machine cost-optimal and throughput-optimal solutions are unique and orderable, and the multi-machine optimal solutions have appealing structure. Furthermore, we establish equivalence between the two formulations and provide an illustrative numerical example.