We establish lower bounds on the minimum costs of managing certain production-distribution networks with setup costs at all stages and stochastic demands. These networks include serial, assembly, and one-warehouse multi-retailer systems. We obtain the bounds through novel cost-allocation schemes. We evaluate the bounds' performance for one-warehouse multi-retailer systems by comparing them with simple, heuristic policies. The bounds are quite tight for systems with a small number of retailers. We also present simplified proofs of known optimality for serial and assembly systems.
Chen, Fangruo, and Yu-Sheng Zheng. "Lower bounds for multi-echelon stochastic inventory systems." Management Science 40, no. 11 (November 1994): 1426-1443.
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