An inventory with partial replenishment subject to compound Poisson demands

Abstract

We introduce a concept of partial replenishment to an inventory. The stock of the inventory is replenished either fully with probability p or partially with probability 1 - p by a deliveryman arriving at the inventory according to a Poisson process. The demands for stock to the inventory form a compound Poisson process. The stationary distribution and the expectation of the level of the inventory are derived. An optimization is studied after several management costs are assigned to the inventory. Significance: We generalize well-known (s,S) policy by adding a concept of partial replenishment. Our policy can be applied to the case where the demands for stock occur according to a Poisson process and the full supply of the stock is not always possible, such as storages of munitions.