The optimal repair policy for an unreliable production system with limited available spare parts

In this study, a serial production system consisting of two machines and an intermediate finite buffer is considered. The machines have random processing times, and each machine contains one unit of a common critical component that is subject to random breakdown. Broken components must be replaced from an inventory of ready-for-use spare parts to restore machine functionality. This inventory is replenished according to a one-for-one replenishment policy with an externally given base stock level. Due to the limited availability of spare parts, the sequence in which the machines are to be repaired and whether they should be repaired immediately must be decided. The objective of our study is the maximization of the expected total discounted revenue per time unit over an infinite planning horizon. We model the system as a semi-Markov decision process and characterize the optimal stationary repair policy. We show that the First-Break-First-Repair policy is not optimal and provide numerical evidence that the optimal repair decision depends on the number of units in the buffer and the number of available spare parts. We show that, in some system states, it is optimal to postpone repair of a machine and reserve spare parts for the other machine. Since the optimal repair policy is state dependent and quite complex, we investigate different prioritization heuristics from the literature in a numerical study. Our experiments suggest that heuristics achieve excellent performance in practical settings.