In a serial inventory system without fixed costs, an echelon base-stock policy is known to be optimal if there is no stockout cost at any stage except the last stage. (This was proved for finite-horizon problems by Clark and Scarf (1960)1 and for infinite-horizon problems by Federgruen and Zipkin (1984)2.)
What is known about the case in which there are non-zero stockout costs at upstream stages? Is an echelon base-stock policy known to be optimal or non-optimal?
Whether or not a base-stock policy is optimal, if we assume such a policy is used, are there algorithms for optimizing the base-stock levels, analogous to those by Clark and Scarf (1960) or Chen and Zheng (1994)3?
 Clark, A. J., Scarf, H. (1960). Optimal Policies for a Multi-Echelon Inventory Problem. Management Science. 6(4):475-490.
 Federgruen, A., Zipkin, P. (1984). Computational Issues in an Infinite-Horizon, Multiechelon Inventory Model. Operations Research. 32(4):818-836.
 Chen, F., Zheng, Y-S. (1994). Lower Bounds for Multi-Echelon Stochastic Inventory Systems. Management Science. 40(11):1426-1443.