A fuzzy random EPQ model with fuzzy defective rates and fuzzy inspection errors

In this paper, we consider an economic production quantity (EPQ) model for imperfect production process under fuzzy random variable demand considering inspection errors. Due to the first stage inspection errors, some proportion of defective items are returned because of dissatisfaction of the customers. In the previous traditional models, the defective rates and the inspection errors follow some probability distributions. However, in real life situation, it is almost impossible to obtain the statistical information precisely. Thus, this study proposes the fuzzy defective rates and the fuzzy inspection errors. In addition, this model interpolates two more stages of inspections, one is after the production run time, and another is after the beginning of the rework process. The purpose of this study is to establish a fuzzy random EPQ model with the fuzzy defective rates and inspection errors. The expected profit per unit time is calculated by using fuzzy random renewal reward theorem. This model maximizes the expected profit per unit time in fuzzy sense. We develop a methodology for finding the global optimal solutions. A numerical example is also provided to illustrate our proposed model. Furthermore, sensitivity analysis is also carried out in order to present some managerial inferences.