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Asymptotically Optimal Inventory Control for Assemble-to-Order Systems with Identical Lead Times

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  • Martin I. Reiman

    (Alcatel-Lucent Bell Labs, Murray Hill, New Jersey 07974)

  • Qiong Wang

    (Industrial and Enterprise Systems Engineering, University of Illinois at Urbana–Champaign, Urbana, Illinois 61801)

Abstract

Optimizing multiproduct assemble-to-order (ATO) inventory systems is a long-standing difficult problem. We consider ATO systems with identical component lead times and a general “bill of materials.” We use a related two-stage stochastic program (SP) to set a lower bound on the average inventory cost and develop inventory control policies for the dynamic ATO system using this SP. We apply the first-stage SP optimal solution to specify a base-stock replenishment policy, and the second-stage SP recourse linear program to make allocation decisions. We prove that our policies are asymptotically optimal on the diffusion scale, so the percentage gap between the average cost from its lower bound diminishes to zero as the lead time grows.

Suggested Citation

  • Martin I. Reiman & Qiong Wang, 2015. "Asymptotically Optimal Inventory Control for Assemble-to-Order Systems with Identical Lead Times," Operations Research, INFORMS, vol. 63(3), pages 716-732, June.
    • Handle: RePEc:inm:oropre:v:63:y:2015:i:3:p:716-732
    DOI: 10.1287/opre.2015.1372
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    References listed on IDEAS

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    2. de Kok, Ton & Grob, Christopher & Laumanns, Marco & Minner, Stefan & Rambau, Jörg & Schade, Konrad, 2018. "A typology and literature review on stochastic multi-echelon inventory models," European Journal of Operational Research, Elsevier, vol. 269(3), pages 955-983.
    3. ElHafsi, Mohsen & Fang, Jianxin & Hamouda, Essia, 2020. "A novel decomposition-based method for solving general-product structure assemble-to-order systems," European Journal of Operational Research, Elsevier, vol. 286(1), pages 233-249.
    4. Levi DeValve & Saša Pekeč & Yehua Wei, 2020. "A Primal-Dual Approach to Analyzing ATO Systems," Management Science, INFORMS, vol. 66(11), pages 5389-5407, November.
    5. Xingxing Chen & Jacob Feldman & Seung Hwan Jung & Panos Kouvelis, 2022. "Approximation schemes for the joint inventory selection and online resource allocation problem," Production and Operations Management, Production and Operations Management Society, vol. 31(8), pages 3143-3159, August.
    6. Jinzhi Bu & Xiting Gong & Xiuli Chao, 2023. "Asymptotic Optimality of Base-Stock Policies for Perishable Inventory Systems," Management Science, INFORMS, vol. 69(2), pages 846-864, February.
    7. Karaarslan, Gönül A. & Atan, Zümbül & de Kok, Ton & Kiesmüller, Gudrun P., 2018. "Optimal and heuristic policies for assemble-to-order systems with different review periods," European Journal of Operational Research, Elsevier, vol. 271(1), pages 80-96.
    8. Martin Albrecht, 2021. "Component Allocation in Make-to-stock Assembly Systems," SN Operations Research Forum, Springer, vol. 2(2), pages 1-19, June.
    9. Lijian Lu & Jing‐Sheng Song & Hanqin Zhang, 2015. "Optimal and asymptotically optimal policies for assemble‐to‐order n‐ and W‐systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(8), pages 617-645, December.
    10. Willem van Jaarsveld & Alan Scheller-Wolf, 2015. "Optimization of Industrial-Scale Assemble-to-Order Systems," INFORMS Journal on Computing, INFORMS, vol. 27(3), pages 544-560, August.
    11. Albrecht, Martin, 2017. "Optimization of safety stocks in models with an order service level objective or constraint," European Journal of Operational Research, Elsevier, vol. 263(3), pages 900-909.
    12. Atan, Zümbül & Ahmadi, Taher & Stegehuis, Clara & Kok, Ton de & Adan, Ivo, 2017. "Assemble-to-order systems: A review," European Journal of Operational Research, Elsevier, vol. 261(3), pages 866-879.
    13. Xin Chen & Menglong Li, 2021. "Discrete Convex Analysis and Its Applications in Operations: A Survey," Production and Operations Management, Production and Operations Management Society, vol. 30(6), pages 1904-1926, June.
    14. David A. Goldberg & Martin I. Reiman & Qiong Wang, 2021. "A Survey of Recent Progress in the Asymptotic Analysis of Inventory Systems," Production and Operations Management, Production and Operations Management Society, vol. 30(6), pages 1718-1750, June.

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