Steady State Analysis of Continuous Review Inventory Systems: A Level Crossing Approach

We consider a continuous review inventory system that faces two different cases of demand processes. In one case demand follows a compound Poisson process. In the other case demand is a combination of a constant deterministic component and a random component which follows a compound Poisson process. We assume negligible lead time. Orders occur when inventory level drops to or below level zero, at which point the inventory is replenished to an order-up-to level S. A level crossing approach is used to derive the steady state distribution of inventory level for each demand scenario. We use the steady state distributions to derive the total expected cost functions and determine the optimal order-upto levels. We ran computational experiments and compared the optimal order-up-to levels from our models to the traditional EOQ. We find that the EOQ overestimates the optimal order-up-to level and in many cases is a poor approximation to the optimal.