Optimal Policies for Assembly Systems with General Initial States

Rosling (1989), one of the classic papers in inventory theory, studies an assembly system with stochastic demand. Under the condition that the initial state of the system possesses a certain property referred to as "long-run balance," the optimal policy is characterized as a balanced echelon base-stock policy. For the same model, we characterize the optimal policy starting with an arbitrary initial state, thereby completing the optimal policy description of Rosling (1989). The optimal policy is also a balanced echelon base-stock policy, 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 (items are indexed by their total lead time), which is a milder condition than the long-run balance condition and is easy to state and verify. In addition, for the two-component assembly system considered by Schmidt and Nahmias (1985), we show that the optimal policy is equivalent to a dynamic balanced echelon base-stock policy