| We consider a two-echelon supply chain with two retailers and one supplier. The retailers order from the supplier who makes all the decisions and bears all the inventory risk. Throughout this thesis, we consider two different inventory systems: a reserved inventory system and a pooled inventory system. With the reserved inventory system, the supplier keeps separate inventories for each retailer. In contrast, the pooled inventory is shared by the two retailers, and the supplier makes the inventory decision based on the joint demand.; First, assuming a fixed wholesale price, we analyze the supplier's decisions in the reserved and the pooled inventory systems. We compare the profit of the supplier and retailers in the two systems under normally distributed demands. We also analyze the scenarios in which the retailers have service level requirements. We find that regardless of whether retailers have service level requirements, under the normally distributed demands, the profits of the supplier and retailers all increase after pooling inventory.; Then, we analyze the scenarios in which the wholesale prices are supplier's decision variables and demand is a function of the wholesale price. We analyze both the additive and multiplicative demands models. We again analyze the supplier's decision on the inventory levels and wholesale price with and without service level requirements. We also compare the profits of the retailers and supplier for the different policies under normally distributed demands. We find that the supplier's profit always increases after pooling the inventory while the retailers's profit may increase or decrease, depending on the system parameters.; This thesis first studies the single period model, and then extends the results to finite and infinite horizon problem with either backlogging or lost sales assumptions. We give mathematical analysis of the pooled and the reserved inventory systems for the infinite horizon case and use simulation methods to compare these two different inventory systems for the finite horizon case. |
