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

In the reliability literature, there are studies that jointly study maintenance and production and that is typically restricted to one failure mode, and fail to address the case where multiple failure modes exist. This study in-vestigates the problem of joint optimization of lot sizing and maintenance policy for a multi-product produc-tion system subject to two failure modes. The failure of the first mode refers to the soft failure that occurs af-ter defects arrive. The failure of the second mode is a hard failure that occurs without any early warning sig-nals. 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 set-up point depend on the lot sizes of products. Models are proposed for two maintenance policies: 1) arranging the maintenance to be at the end of each production cycle; 2) arranging the maintenance to be at set-up points. The expected profit per unit time is formulated to obtain the optimal lot sizing and maintenance policy. Some properties of proposed models are proved, which show that the optimal lot sizing and mainte-nance policy can be obtained under certain conditions. Case studies and sensitivity analyses are presented to illustrate the proposed models of two maintenance policies. Basically, the results show that the producer 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 economic. The sensitivity analyses il-lustrate that reducing the cost caused by failures and improving system reliability are effective ways to in-crease the expected profit per unit time.