The economic production quantity model for an imperfect production process by control chart design

The Economic Production Quantity (EPQ) plays a crucial role in the manufacturing process. The traditional EPQ model operates under the assumption that Non-Conforming (NC) items are not produced, and the process remains under control. However, real-world scenarios often involve the production of NC products, leading to process deviations. This study introduces a model that optimizes the design of a control chart to incorporate NC products into the EPQ model. The model integrates inventory and quality-related costs to minimize the expected total cost by determining EPQ, sample size, and control limit. The solution methodology employs direct search techniques to solve this problem. The sensitivity analysis results demonstrate the significant cost reduction achieved by the proposed model compared to the classical EPQ model. The numerical examples presented in the study show an average cost reduction of approximately 21 percent, highlighting the potential effectiveness of the model in cost reduction efforts.