The replenishment policy for an inventory system with Poisson arrival demands

The consumers arrive at a store according to a Poisson process and purchase a stochastic quantity of resources. A store with a bounded tank is forced to follow reasonable management in a balance between surplus orders and shortages. In this paper, we consider an inventory replenishment policy that the store establishes safety stock quantities to minimize the expected costs per unit time, and that it replenishes the stock at the time fallen to the safety stock level so as to keep the losses of costs for shortages and excess orders to a minimum. We also present a numerical example for the case that demand follows the exponential distribution.