Fast approach to the optimal production/PM policy

We study the economical manufacturing quality (EMQ) problem in the presence of an imperfect process. When the production process goes out of control, the production process produces some proportion of defective items. Thus, lot sizing and periodic inspection of the process are needed to operate the system economically. Performing a preventive maintenance (PM) action immediately after inspection and possible adjustment of the production process will be helpful to enhance the process reliability of a deteriorating production system; thus, an EMQ model for inspection/PM was proposed in the literature. However, it is not easy to derive the optimal lot sizing and inspection/PM policy simultaneously. Therefore, a two-dimensional search procedure is needed to find the optimal production/PM scheme. In this paper, we study the structural properties of the production/PM problem and show the uniqueness of the optimal inspection interval for a given number of inspections in a production run. To solve the production/PM problem, we provide lower and upper bounds for the optimal inspection interval when the number of inspections is given during a production run and use them to reduce the search ranges in a numerical solution procedure. Also, a criterion for stopping the process of searching for the optimal production/PM policy is provided.