Capacitated Multiechelon Inventory Systems: Policies and Bounds

We study a periodically reviewed multiechelon serial inventory system with a capacity constraint on the order quantity at each stage. The cost criterion we use to evaluate inventory policies for this system is the sum of the expected long‐run average holding and shortage costs. It is well known that for this problem, characterizing the structure of the optimal policy and computing it are very difficult. We consider the use of echelon base‐stock policies for our system (even though they are known to be suboptimal) and propose algorithms for finding base‐stock levels that are easy to understand and implement. We derive bounds on the ratios between the costs achieved by our algorithms and the optimal costs (over all policies). For light‐tailed demand distributions, our algorithms are shown to be asymptotically optimal in the sense that our bounds are close to one in high service‐level environments. Our computational investigations reveal that our algorithms perform well even under modest service levels.