Production-inventory systems with preventive maintenance

We consider a production facility that produces items for which demand occurs according to a Poisson process. The facility is assumed to deteriorate while it is in operation, with an increasing failure rate. A preventive maintenance overhaul of the facility is, however, assumed to restore it to its original condition. We consider the following control policy for operating the facility: as soon as the inventory level is raised to a certain prespecified value, S, a preventive maintenance operation is initiated. After the preventive maintenance operation, production resumes as soon as the inventory level drops down to or below another prespecified value, s, and the facility continues to produce items until the inventory level is raised back to S. If the facility breaks down during operation, it is minimally repaired and put back into commission. Under a cost structure that includes a preventive maintenance cost, a repair cost, a setup cost, a holding cost, and a backorder cost, an expression for the expected cost per unit time is obtained for a given policy. Some properties of the cost functions are developed to characterize the optimal policy. On the basis of these properties, an efficient algorithm to find the optimal policy is presented.