Dedicated maintenance and repair shop control for spare parts networks

We study a repairable inventory system for a single capital good and for multiple capital goods, where each good has one critical component, its own stock point, and a shared capacitated repair shop. The system consists of stock points that are controlled according to a base stock policy and a dedicated repair shop that has finite capacity. The component is replaced from stock either preventively if it reaches an age threshold or correctively upon failure. The time between failures has a general distribution. If a spare component is not available in stock, the capital good becomes inoperable and a downtime cost is incurred. The objective is to decide the base stock level, the age-threshold, and the repair shop's capacity that minimize the total cost (corrective, downtime, inventory, and repair capacity cost). We show that this inventory system resembles a closed queueing network which enables us to derive an exact cost expression. For the system with multiple components, we consider different priority policies in the repair shop. Numerical results show that there is an inherent trade-off: a low (high) age-threshold reduces (increases) the probability of a corrective replacement but increases (decreases) the demand for repair capacity, and a high (low) number of repairables in the system leads to higher (lower) holding costs, but decreases (increases) the probability of downtime.