Jointly optimizing lot sizing and maintenance policy for a production system with two failure modes

In the reliability literature, studies that jointly investigate maintenance and production are typically restricted to one failure mode and fail to address the case where multiple failure modes may exist. This study investigates the problem of joint optimization of lot sizing and maintenance policy for a multi-product production system subject to two failure modes. The failure of the first mode is a soft failure that occurs after defects arrive. The failure of the second mode is a hard failure that occurs without any early warning signals. Products are sequentially produced by the system and a complete run of all products forms a production cycle. The system needs to be re-set up before producing a different product. Both the production cycle and the time of set-up depend on the lot sizes of products. Models are proposed for two maintenance policies: 1) arranging the maintenance during the set-up at the end of each production cycle; 2) arranging the maintenance during each of set-ups. The expected profit per unit time is formulated to obtain the optimal lot sizing and maintenance policy. Some properties of the proposed models are provided and they show that the optimal lot sizing and maintenance policy can be obtained under certain conditions. Case studies and sensitivity analyses are presented to illustrate the proposed models of two maintenance policies. The results show that the manufacturer will gain the most profit if the optimal lot sizing and maintenance policy are adopted. The results of comparing both maintenance policies reveal that the excessive maintenance is not cost-effective. The sensitivity analyses illustrate that reducing the cost due to failures and improving system reliability are effective ways to increase the expected profit per time unit.