Optimal lot sizing in screening processes with returnable defective items


1 Young Researchers and Elite Club, Islamic Azad University, Qazvin Branch, Qazvin, Iran

2 Department of Industrial Engineering, Sharif University of Technology, P.O. Box 11155-9414, Azadi Ave., 1458889694, Tehran, Iran

3 Department of Industrial and Mechanical Engineering, Islamic Azad University, Qazvin Branch, Qazvin, Iran

4 Department of Industrial Engineering, Islamic Azad University, South Tehran Branch, Tehran, Iran


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 renewalreward
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.