An integrated optimization of lot-sizing and condition-based maintenance policy of a two-stage deteriorating system

In this study, a two-stage deteriorating production system is considered. The initiation time of the deterioration follows an exponential distribution. A homogeneous Gamma process is used to model the deterioration propagation process. The equipment produces a single product with a constant production rate and demand rate. To ensure the efficiency of the production, inspection is carried out at the end of each production run. The lot-sizing and the condition-based maintenance threshold are optimized by minimizing the long-run average cost rate, which is derived in the framework of a semi-Markov decision process. The traversal algorithm is used to obtain optimal results. A numerical example is presented to illustrate the applicability of the proposed model. Some sensitivity analysis are carried out in order to highlight the interest and properties of the model. It may provide a theoretical reference for production and maintenance schedules.