Lower Bounds for Multi-Echelon Stochastic Inventory Systems

We establish lower bounds on the minimum cost 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 proof of known optimality results for serial and assembly systems.