Optimal lot sizing in screening processes with returnable defective items

This paper is an extension of Hsu and Hsu (Int J Ind Eng Comput 3(5):939–948, 2012) aiming to determine the optimal order quantity of product batches that contain defective items with percentage nonconforming following a known probability density function. The orders are subject to 100 % screening process at a rate higher than the demand rate. Shortage is backordered, and defective items in each ordering cycle are stored in a warehouse to be returned to the supplier when a new order is received. Although the retailer does not sell defective items at a lower price and only trades perfect items (to avoid loss), a higher holding cost incurs to store defective items. Using the renewal-reward theorem, the optimal order and shortage quantities are determined. Some numerical examples are solved at the end to clarify the applicability of the proposed model and to compare the new policy to an existing one. The results show that the new policy provides better expected profit per time.