Inventory policies in a decentralized assembly system

We consider a system in which a single finished good is assembled from two components. Demand for the finished product is stochastic and stationary, and procurement and assembly lead times are constant. Unsatisfied demand is backordered. The inventory of each component or assembly is controlled by a separate firm using a base-stock policy. Each firm is charged holding costs on its own inventory, plus a share of the shortage cost due to backorders of the finished product. We investigate the equilibrium base-stock levels that arise in this system under both echelon and local base-stock policies. In both cases, the component firms' base-stock levels are economic complements. We then examine the effect on system performance when one firm uses information about other firms' pipeline inventory. We find that, under echelon base-stock policies, all firms benefit with the use of pipeline information. In contrast, under local policies, using pipeline information may actually increase costs for some firms (including the firm that makes direct use of the information). Also, we compare the behavior of the decentralized system with that of the assembly system under centralized control. Finally, we describe a payment scheme between the final assembler and the suppliers that allows the decentralized system to achieve the centralized solution.