Inventory and Service System in a Two-Echelon Supply Chain Using Base Stock Policy

In this paper we consider a two-echelon supply chain system consisting of a supplier and a retailer. The supplier has an inventory system and a service unit to process the orders received from the retailer. Demands arrive to the retailer according to a Poisson process. Both supplier and retailer apply one-for-one ordering policy. The supplier’s lead time and the service time of his service unit are exponentially distributed random variables. When the supplier has on-hand inventory, the retailer’s order joins the queue at the service unit. Otherwise the supplier does not accept retailer’s order. In this paper we first derive the steady state joint distributions of the “queue length” and “on-hand inventory of the supplier” and show that it has a product form. Furthermore, we derive the total expected system cost per unit time. Finally by a numerical example we obtain the optimal solution of the total system cost.