An economic order quantity model with screening errors, returned cost, and shortages under quantity discounts

Previous studies on the issue of imperfect quality inventory assumed the direct cost of the product was irrelevant and the screening processes were perfect. However, in practice, the purchase price is some function of the quantity purchased and the inspection testing may fail to be perfect due to Type 1 and Type 2 errors. Thus, this paper proposes a cost-minimizing Economic Order Quantity (EOQ) model that incorporates imperfect production quality, inspection errors (including Type 1 and 2), shortages backordered, and quantity discounts. It is assumed that production, in which 100% screening processes are performed with possible inspection errors, is received with defective quality items and the supplier offers all-unit quantity discounts to the buyer. An algorithm is developed to determine the optimal lot size, shortages and purchase price. Three numerical examples are provided to illustrate the proposed model and algorithm. Numerical computations show that the algorithm is intuitively simple and efficient. Managerial insights are also drawn.