Analysis of order-up-to-level inventory systems with compound Poisson demand

We analyse a single echelon single item inventory system where the demand and the lead time are stochastic. Demand is modelled as a compound Poisson process and the stock is controlled according to a continuous time order-up-to level policy. We propose a new method for determining the optimal order-up-to level for a cost oriented inventory systems where unfilled demands are backordered. The conditions under which the system behaves like a Make-To-Order setting are also discussed. By means of a numerical investigation, we show that the proposed method provides very good results. It is also shown to outperform another approximate solution provided in the literature. Our work allows insights to be gained on stock control related issues for both fast and slow moving Stock Keeping Units.