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.