estimation of the cost function of a two-echelon inventory system with lost sales using regression

multi-echelon inventory systems are one of the most important and attractive areas in modelling supply chain management so that several researches and studies have been done about. in this paper, the total cost function of a two-echelon inventory system with central warehouse and many identical retailers controlled by continuous review inventory policy is estimated. we have assumed the demand in the retailers experiences independent poisson distribution and unsatisfied demands are lost in the retailers and unsatisfied retailer order is backordered in the central warehouse. the transportation time from warehouse to each retailer and the lead time of the warehouse orders are assumed to be constant. the accuracy of the estimation is assessed by simulation. the main contribution of this paper is using statistical tools in two-echelon inventory systems analysis.