Lower Bounds for Multi-echelon Stochastic Inventory Systems

e establish lower bounds on the minimum costs of managing certain productiondistribution 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 results for serial and assembly systems. (Stationary Analysis; Cost Allocation; Economies of Scale; Multi-stage Production Systems; Distribution Networks; Replenishment Strategies)