Optimal Policies for Assembly Systems : Completing Rosling's Characterization

We study an assembly system with stochastic demand. This is the model studied in Rosling (1989), one of the classic papers in inventory theory, where the optimal policy is characterized as a balanced echelon base-stock policy, assuming that the initial state of the system possesses a certain property referred to as 'long-run balance.' We characterize the optimal policy starting with any arbitrary initial state, thereby completing the optimal policy description of Rosling (1989). The optimal policy is essentially a balanced echelon base-stock policy again, but with dynamically evolving echelon base-stock levels. We also show that the policy prescribed by Rosling (1989) is still optimal, if the initial echelon inventory positions are non-decreasing in item index, which is a milder condition than the long-run balance assumption and is easy to state and to check