An economic production quantity inventory model with a defective production system and uncertain uptime

In this study, a fuzzy mathematical programming for an inventory system with defective items is considered. The system consists of a single machine that requires maintenance to enhance its efficiency, performance and lifespan. Due to the environmental uncertainties, uptime is estimated based on the linguistic variables, i.e., experts' opinions. So, the inherited uptime is a fuzzy number in trapezoid form, i.e., machine works certainly up to a time and it fails with an optimistic and pessimistic estimation. Moreover, machinery should go through a preventive maintenance procedure during downtime. The proposed model helps production managers to reduce system costs by improving machine efficiency and performance employing appropriate maintenance policies. To solve the proposed problem, we optimise system costs by calculating optimum production cycle using an algorithm to calculate upper and lower bounds of inherited crisp problem. Finally, a numerical example is represented to investigate the effectiveness of the proposed algorithm.