Joint reserve stock and just-in-time inventory under regular preventive maintenance and random disruptions

We study a repairable production-inventory system with a constant demand rate subject to random disruptions, which supplies an assembly line according to a just-in-time configuration. Preventive maintenance (PM) actions are regularly performed on the production unit at fixed time instants. We assume that the time between breakdowns is constant and the PM and corrective actions have random durations that follow a general probability distribution. We propose the following policy to cope with production interruptions: A buffer stock is built up at the maximum production rate at the beginning of each PM cycle. At the same time, a reserve stock is maintained to hedge against random disruptions and shortages during planned maintenance. The joint convexity of the cost function is established and optimality conditions for the optimal policy parameters are derived. We perform numerical and sensitivity analyses under the exponential and Asymmetric Laplace distributions. The results suggest that: (i) The proposed policy performs better than traditional models that consider these two strategies separately; (ii) As the shortage cost increases, it is optimal to increase the reserve level; (iii) Higher reserve stock levels allow to hedge against the increased duration and rate of preventive maintenance and random disruptions.