Joint determination of production cycle and preventive maintenance schedule for an imperfect production system under stochastic demand

This paper deals with integrating lot‐sizing decisions in stochastic continuous review inventory control model and preventive maintenance (PM) decisions for an imperfect process having a general deterioration distribution with increasing hazard rate. The demand on the produced item is a random variable that follows a normal distribution. Furthermore, the production process under consideration is imperfect, that is, it may fail at any point in time during the production run. If it suddenly fails while engaged in production, the process is minimally repaired without affecting its age. In order to reduce the occurrences of such sudden failures, preventive maintenance (PM) is carried out at certain intervals of time during the production run. The PM policy considered here reduces the age of the process by a certain amount depending on the cost of PM conducted. The objective of the model is to determine the optimal lot size and maintenance schedule such that the expected total cost is minimised.