Research on two-echelon distributed inventory model with lost sales at a central warehouse

We consider a two-echelon distributed inventory system with one warehouse and several retailers. Adopting a (S1,S) base-stock policy, we use a queuing system and METRIC approximation synthetically as a framework, which presents a two-echelon inventory management model with lost sales at a central warehouse. With stockout at the central warehouse, many retailers cannot wait for backorder, so they then order with supplier, which will lead to opportunity cost due to lost sale at the central stocking point.