Cost evaluation of a two-echelon inventory system with lost sales and approximately Poisson demand

The inventory system under consideration consists of one central warehouse and many identical retailers controlled by continuous review inventory policy (R,Q). We assume independent Poisson demands with constant transportation times for the retailers and a constant lead time for replenishing orders from an external supplier for the warehouse. Unsatisfied demands are assumed to be lost in the retailers and unsatisfied retailer orders are backordered in the warehouse. We develop an approximate cost function to find optimal reorder points for given batch sizes in all installations and the related accuracy is assessed through simulation.