Stock-out policies of a spare-parts warehouse for a multi-item repairable system

In industrial settings, the management of spare-parts inventory can have a significant impact on the system's reliability and profitability. In this paper, we provide a framework that jointly optimises reliability of a multi-item system and the management of an accompanying spare-parts warehouse (SPW) with a finite capacity. Consider a system with N items that operate in parallel and have random life spans; when an item breaks, it is replaced by a spare part (if available) with no time. The SPW is managed according to a continuous-review (Formula presented.) policy. That is, when the number of spare parts drops to level (Formula presented.), an order is placed to replenish the warehouse to level S after a random lead time. When a spare part is unavailable, the company chooses between two stockout policies: a cold standby policy or an emergency supply policy. Using the matrix-geometric method for phase-type distributions, we derive the optimal thresholds minimising the expected discounted total cost (including replacement, replenishment, maintenance, downtime, and emergency supply costs). Using a numerical study, we compare the policies and provide managerial insights. For example, we show that an emergency supply policy may yield a significant cost reduction, particularly for high maintenance cost and long lead times.