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. this paper presents a production inventory model that considers the inspection of the produced batches and disposal of defective items in an economic production quantity (epq) model with partial backorders and a discount on batches that are imperfect but not defective. furthermore, the proposed model also considers the holding cost of these imperfect items while they are not sold. a step-by-step is conducted to find the optimal solution and a numerical example is provided to perform sensitivity analysis. we conclude that the setup cost and the holding cost are the ones with the most significant impacts on the total cost function. 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.