EPQ model with inspection of batches and disposal of defective items

Manufacturing processes can produce imperfect items, and inventory disruptions may occur in the process, causing shortages. We propose a model to explore these real-life scenarios. This paper offers a production inventory model considering the concept of inspection of the produced batches and disposal of defective items in an Economic Production Quantity (EPQ) model with partial backorders and discount on batches that are imperfect but not defective. Furthermore, the proposed model considers the holding cost of these imperfect items while they are not sold. An algorithm for finding the optimal solution is presented, and a numerical example is provided to perform a sensitivity analysis. We conclude that the setup cost followed by the holding cost are the costs that have the most significant impact on the total cost. Although the inspection cost has been added to the model, this cost has little effect on the total cost and does not increase it significantly.