This paper considers a continuous review perishable inventory system with demands arrive according to a Markovian arrival process (MAP). We model, in this paper, the situation in which not all the ordered items are usable and the supply may contain a fraction of defective items. The number of usable items is a random quantity. We consider a modified (s, S) policy which allows a finite number of pending order to be placed. We assume full backlogging of demands that occurred during stock out periods and that the recent backlogged demand may renege the system after an exponentially distributed amount of time. The limiting distribution of the inventory level is derived and shown to have matrix geometric form. The measures of system performance in the steady state are derived.