A stochastic program based lower bound for assemble-to-order inventory systems

Martin I. Reiman, Qiong Wang

Research output: Contribution to journalArticlepeer-review


In this paper 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 Doru et al. (2010) [3] 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.

Original languageEnglish (US)
Pages (from-to)89-95
Number of pages7
JournalOperations Research Letters
Issue number2
StatePublished - Mar 1 2012
Externally publishedYes


  • Assemble-to-order (ATO)
  • Inventory
  • Multi-dimensional newsvendor model
  • Optimal policy
  • Stochastic program

ASJC Scopus subject areas

  • Software
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering
  • Applied Mathematics

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