Performance evaluation and stock allocation in capacitated serial supply systems

We develop an approximation scheme for performance evaluation of serial supply systems when each stage operates like a single-server queue, and its planned inventories are managed according to a base-stock policy. We also present a near-exact matrix-geometric procedure for benchmarking our approximation relative to two other methods proposed in the literature. Through numerical tests, we demonstrate that our method is superior, both for performance estimation and for policy parameter optimization. Using this technique, we then perform experiments that address the following issues. What proportion of the optimal total inventory should managers allocate to upstream production stages to minimize the sum of inventory and backorder costs? If managerial action could lower holding cost rate or add capacity, which stages of the supply system should be targeted for maximum net benefit? Such concerns have been the subject of several recent studies relating to supply networks with constant and random independent lead times. We shine light on optimal actions for serial supply systems that experience congestion.