Linear and nonlinear estimation of the cost function of a two-echelon inventory system

The inventory system under consideration consists of one central warehouse and a few non-identical retailers controlled by a continuous review inventory policy (image). The retailers face an independent Poisson demand. Order transportation time from the central warehouse to each retailer is assumed to be constant. Also, the lead time for replenishing orders from an external supplier is assumed to be constant for the warehouse. Unsatisfied demands are assumed to be lost at the retailers and unsatisfied retailer orders are backordered at the warehouse. The cost function of the system was estimated utilizing a Response Surface Method (RSM) in the case of four retailers, and, in this regard, two linear and nonlinear regression models were developed. The optimal reorder points for given batch sizes in all installations were obtained from optimizing the estimated cost function. The estimation accuracy was assessed through simulation. The results indicate that the nonlinear regression model outperforms the linear one.