Decentralized inventory control in a two-component assembly system

We investigate a two-component assembly system facing stationary stochastic demand with constant component replenishment lead times. Holding costs are charged for each component inventory, which are managed by component suppliers; final product demand is backordered when it cannot be fulfilled in time and a penalty cost is charged. We assume the long lead-time component supplier takes normal base-stock policy while the short lead-time component supplier takes a modified base-stock policy. Static game and Stackelberg games are considered. Equilibria are analyzed and the costs in equilibria are compared with the system optimal solution, difference shows the deterioration of system performance caused by decentralized inventory control. We try to design a mechanism to coordinate the decentralized system, that is to make decentralized system perform as well as system optimal solution though the decisions separated. We show that a linear transfer based on the backorder between the component suppliers qualifies this task.