Fuzzy EPQ models for an imperfect production system

Manufacturing uncertainties are inevitable as unexpected events may occur at any time. In this article, we consider an imperfect production system in which the production process may shift from the in-control state to the out-of-control state at any random time. We assume that the fraction of defective items produced after process shift is uncertain and can be characterised by a fuzzy number. In another attempt, we take the fraction of defective items produced as a random variable, which follows an exponential probability distribution with fuzzy parameter. The expected fuzzy cost per unit time is derived in each model and defuzzified by using centroid method to obtain crisp values that can be used for comparison purposes. Two numerical examples are taken to demonstrate the optimal results of the proposed fuzzy models numerically and to compare these results with the corresponding ones in crisp models.