Asymptotically Optimal Inventory Control for Assemble-to-Order Systems

Martin I. Reiman, Haohua Wan, Qiong Wang

Research output: Contribution to journalArticlepeer-review


We consider assemble-to-order (ATO) inventory systems with a general bill of materials and general deterministic lead times. Unsatisfied demands are always backlogged. We apply a four-step asymptotic framework to develop inventory policies for minimizing the long-run average expected total inventory cost. Our approach features a multistage stochastic program (SP) to establish a lower bound on the inventory cost and determine param-eter values for inventory control. Our replenishment policy deviates from the conventional constant base stock policies to accommodate nonidentical lead times. Our component allocation policy differentiates demands based on backlog costs, bill of materials, and component availabilities. We prove that our policy is asymptotically optimal on the diffusion scale, that is, as the longest lead time grows, the percentage difference between the average cost under our policy and its lower bound converges to zero. In developing these results, we formulate a broad stochastic tracking model and prove general convergence results from which the asymptotic optimality of our policy follows as specialized corollaries.

Original languageEnglish (US)
Pages (from-to)128-180
Number of pages53
JournalStochastic Systems
Issue number1
StatePublished - Mar 2023


  • assemble-to-order
  • asymptotic optimality
  • inventory management
  • stochastic program
  • stochastic tracking model

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty
  • Management Science and Operations Research


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