The Cost Function for a Two-warehouse and Three-Echelon Inventory System

In this paper, the cost function for a three-echelon inventory system with two warehouses is derived. Transportation times are constant and retailers face independent Poisson demand. Replenishments are one-for-one. The lead time of a retailer is determined not only by the constant transportation time but also by the random delay incurred due to the availability of stock at the warehouses. We consider two warehouses in the second echelon which may leads to having more delays which were incurred in the warehouses and facing different behaviors of independent Poisson demands. Because the replenishment policy is base stock, the obtained function can also be used in different ordering policies to compute the inventory holding and shortage costs.