Cost evaluation of a two-echelon inventory system with lost sales and non-identical retailers

The inventory system under consideration consists of one central warehouse and an arbitrary number of non-identical retailers controlled by continuous review policy(R,Q). It is assumed Independent Poisson demands with constant transportation times for the retailers and constant lead time for replenishing orders from an external supplier for the warehouse. Unsatisfied demands are assumed lost at the retailers and unsatisfied retailer orders are backordered at the warehouse. An approximate cost function is developed to find optimal reorder points for given batch sizes in all installations and the related accuracy is assessed through simulation. The proposed method is an extension to the approximate assumption of Poisson demand on the warehouse previously and adds more approximations to tackle retailer's lead time complexity.