The economic production quantity model with optimal single sampling inspection

This paper derives an inspection policy for an economic production quantity (EPQ) model under the assumption that a process may produce non-conforming (NC) items. In various stages of a production process, a department receiving an order uses a single sampling inspection policy to detect NC items. Under such a policy, a lot is accepted if the number of NC items in the inspected sample is equal to or less than the acceptance number. The proposed model considers both EPQ- and quality-related costs. Moreover, economic production order quantity, sample size, and acceptance number are considered decision variables. A numerical example is presented, and a set of sensitivity analysis are provided to highlight the effectiveness of the proposed model. The results reveal that when the inspection cost is high, the classical EPQ model achieves a lower expected total cost for the production system compared to the EPQ model with the inspection. In contrast, when the NC cost is high, the EPQ model with the inspection policy outperforms the classical EPQ model, which can significantly decrease the expected total cost.