In this article, we consider an imperfect production-inventory system which produces a single type of product to meet the constant demand. The system deteriorates stochastically with usage and the deterioration process is modeled by a non-stationary gamma process. The production process is imperfect which means that the system produces some non-conforming items and the product quality depends on the degradation level of the production system. To prevent the system from deteriorating worse and improve the product quality, preventive maintenance is performed when the level of the system degradation reaches a certain threshold. However, the preventive maintenance is imperfect which cannot restore the system as good as new. Hence, the aging system will be replaced by a new one after some production cycles. The preventive maintenance cost, the replacement cost, the production cost, the inventory holding cost and the penalty cost of lost sales are considered in this article. The objective is to minimize the total cost per unit item which depends on two decision variables: the preventive maintenance threshold and the time at which the system is replaced. We derive the explicit expression of the total cost per unit item and the optimal joint policy can be obtained numerically. An illustrative example and sensitivity analysis are given to demonstrate the proposed model.
