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A stochastic program based lower bound for assemble-to-order inventory systems. (English) Zbl 1270.90040
Summary: We introduce a multi-stage stochastic program that provides a lower bound on the long-run average inventory cost of a general class of assemble-to-order (ATO) inventory systems. The stochastic program also motivates a replenishment policy for these systems. Our lower bound generalizes a previous result of M. K. Doğru et al. [Oper. Res. 58, No. 4, Part 1, 849–864 (2010; Zbl 1231.90026)] for systems with identical component replenishment lead times to those with general deterministic lead times. We provide a set of sufficient conditions under which our replenishment policy, coupled with an allocation policy, attains the lower bound (and is hence optimal). We show that these sufficient conditions hold for two examples, a single product system and a special case of the generalized \(W\) model.

MSC:
90C15 Stochastic programming
90B05 Inventory, storage, reservoirs
Citations:
Zbl 1231.90026
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References:
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