A Decomposition Approach for a Class of Capacitated Serial Systems

We study a class of two echelon, serial systems with identical ordering capacities or limits for both echelons. For the case where the lead time to the upstream echelon is one period, the optimality of state-dependent, modified echelon base-stock policies is proved using a decomposition approach. For the case where the upstream lead time is two periods, we introduce a new class of policies called “two-tier, base-stock policies,” and prove their optimality. Some insight about the inventory control problem in N echelon, serial systems with identical capacities at all stages and arbitrary lead times everywhere is also provided. We argue that a generalization of two-tier, base-stock policies, which we call “multi-tier, base-stock policies,” are optimal for these systems; we also provide a bound on the number of parameters required to specify the optimal policy.