Integrating production, maintenance and quality: A multi-period multi-product profit-maximization model

We consider a set of items that must be produced in lots in a capacitated production system. Two types of failures are considered. At the occurrence of Type I failure, the system shifts to an out-of-control state where it produces a fraction of nonconforming items. After a shift, the system is restored to its initial in-control state. With Type II failures, the system stops and it is minimally repaired. During each period, the system is inspected and imperfect preventive maintenance (PM) activities can be performed to reduce its age, proportional to the PM level. At the end of each period a complete repair is performed. We develop an integrated optimization model where the objective is to maximize the expected profit. Computational experiments are performed to analyse the trade-offs between maintenance, quality and production. It is found that the increase in PM level leads to reductions in quality related impacts; but, if the cost of performing PM is high to the point where it is not compensated for by quality improvement, then performing PM is not beneficial. It is also found that using no-periodic inspections with the possibility of non-uniform PM levels may result in an improvement of the total profit.