Perishable inventory system with random supply quantity and negative demands

In this paper we consider a continuous review perishable inventory system with a modified (s, S) policy which allows a finite number of orders to be placed and full backlogging of demands. However the demand that occurred during the stock out period has the option to join the system with prefixed probability. Moreover, we assume two streams of demands called regular and negative. The negative demand during the stock out periods removes one of the waiting demand if any. The limiting distribution of the inventory level is shown to have matrix geometric form. The measures of system performance in the steady state are derived.