The Replenishment Policy for an Inventory System with a Fixed Ordering Cost and a Proportional Penalty Cost under Poisson Arrival Demands

Abstract

A store with a bounded tank sells a random resource to customers arriving according to the Poisson process. It reasonably has to be managed in a balance between a fixed ordering cost and a proportional penalty cost. The store should lay down the safety stock level so as to keep these losses as minimal as possible. Then he adopts an ordering policy in which the tank is filled with resource when the stock level falls to the safety stock level. We decide the optimal safety stock level so as to minimize the expected cost per unit time in the infinite periods.