Optimal lot-sizing problem with imperfect maintenance and imperfect production

In this paper, we develop an integrated model for the joint determination of both economic production quantity and level of preventive maintenance (PM) for an imperfect production process. This process has a general deterioration distribution with increasing hazard rate. The effect of PM activities on the deterioration pattern of the process is modelled using the imperfect maintenance concept. In this concept, it is assumed that after performing PM, the ageing of the system is reduced in proportion to the PM level. After a period of time in production, the process may shift to out-of-control states, either type I or type II. A minimal repair will remove the type I out-of-control state. If a type II out-of-control state occurs, the production process has to stop, and then restoration work is carried out. Examples of Weibull shock models are given to show that the use of PM reduces costs.