A perishable system with modified base stock policy and random supply quantity

We analyse an inventory system with Poisson demands stocking perishable items having constant hazard rates. Orders are placed at every demand epoch so as to take the inventory position back to its maximum level. The replenishment rate depends on the amount on order and the supply quantity which is random. The assumption on demands during stock-out periods cover complete lost sales, partial backordering, and full backlogging as special cases. A matrix recursive scheme is developed to determine the limiting distribution. The computational efficiency of this procedure in the determination of the optimal parameters that minimizes the long run expected cost rate is illustrated with examples.