The effect of supply uncertainty/quality considerations on inventory control has been widely recognized Different assumptions concerning the uncertain supply process have been made.
One stream of research considers a ‘‘stochastically proportional’’ supply where the fraction of
imperfect quality items in a lot is random with a known probability distribution independent of the
order quantity. Earlier work in this stream includes Karlin (1958), Shih (1980), and Silver (1976).
Recent related research includes the work of Salameh and Jaber (2000) who assume that a screening
process is initiated upon the receipt of an order where imperfect items are detected to be sold
later at a discount. Several authors recently adopt Salameh and Jaber’s assumptions on handling of
imperfect quality. In particular, Maddah and Jaber (2008) rectify a flow in Salameh and
Jaber’s model by properly applying renewal theory, while Maddah et al. (2010b), motivated by the
concerns of Papachristos and Konstantaras (2006), propose an order overlapping scheme aimed at
overcoming shortages during screening. In another related work, Maddah et al. (2009) incorporate
a demand and cost structure for imperfect
quality items.