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A Decomposition Approach for a Class of Capacitated Serial Systems

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  • Ganesh Janakiraman

    (IOMS-OM Group, Stern School of Business, New York University, New York, New York 10012)

  • John A. Muckstadt

    (School of Operations Research and Industrial Engineering, Cornell University, Ithaca, New York 14853)

Abstract

We study a class of two-echelon serial systems with identical ordering/production capacities or limits for both echelons. Demands are assumed to be integer valued. For the case where the lead time to the upstream echelon is one period, the optimality of state-dependent modified echelon base-stock policies is proved using a decomposition approach. For the case where the upstream lead time is two periods, we introduce a new class of policies called “two-tier base-stock policies,” and prove their optimality. Some insight about the inventory control problem in N echelon serial systems with identical capacities at all stages and arbitrary lead times everywhere is also provided. We argue that a generalization of two-tier base-stock policies, which we call “multitier base-stock policies,” are optimal for these systems; we also provide a bound on the number of parameters required to specify the optimal policy.

Suggested Citation

  • Ganesh Janakiraman & John A. Muckstadt, 2009. "A Decomposition Approach for a Class of Capacitated Serial Systems," Operations Research, INFORMS, vol. 57(6), pages 1384-1393, December.
    • Handle: RePEc:inm:oropre:v:57:y:2009:i:6:p:1384-1393
    DOI: 10.1287/opre.1080.0680
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Woonghee Tim Huh & Ganesh Janakiraman & Mahesh Nagarajan, 2016. "Capacitated Multiechelon Inventory Systems: Policies and Bounds," Manufacturing & Service Operations Management, INFORMS, vol. 18(4), pages 570-584, October.
    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. Li Chen & Jing-Sheng Song & Yue Zhang, 2017. "Serial Inventory Systems with Markov-Modulated Demand: Derivative Bounds, Asymptotic Analysis, and Insights," Operations Research, INFORMS, vol. 65(5), pages 1231-1249, October.
    4. Awi Federgruen & C. Daniel Guetta & Garud Iyengar, 2018. "Two‐echelon distribution systems with random demands and storage constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(8), pages 594-618, December.
    5. Woonghee Tim Huh & Ganesh Janakiraman, 2010. "On the Optimal Policy Structure in Serial Inventory Systems with Lost Sales," Operations Research, INFORMS, vol. 58(2), pages 486-491, April.
    6. Woonghee Tim Huh & Ganesh Janakiraman, 2010. "Base‐stock policies in capacitated assembly systems: Convexity properties," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(2), pages 109-118, March.
    7. Manafzadeh Dizbin, Nima & Tan, Barış, 2020. "Optimal control of production-inventory systems with correlated demand inter-arrival and processing times," International Journal of Production Economics, Elsevier, vol. 228(C).
    8. Victor Martínez-de-Albéniz & Alejandro Lago, 2010. "Myopic Inventory Policies Using Individual Customer Arrival Information," Manufacturing & Service Operations Management, INFORMS, vol. 12(4), pages 663-672, May.
    9. Woonghee Tim Huh & Ganesh Janakiraman & Mahesh Nagarajan, 2010. "Technical Note ---Capacitated Serial Inventory Systems: Sample Path and Stability Properties Under Base-Stock Policies," Operations Research, INFORMS, vol. 58(4-part-1), pages 1017-1022, August.
    10. Qi Feng & Zhongjie Ma & Zhaofang Mao & J. George Shanthikumar, 2021. "Multi‐Stage Supply Chain with Production Uncertainty," Production and Operations Management, Production and Operations Management Society, vol. 30(4), pages 921-940, April.
    11. Peter Berling & Danja R. Sonntag, 2022. "Inventory control in production–inventory systems with random yield and rework: The unit‐tracking approach," Production and Operations Management, Production and Operations Management Society, vol. 31(6), pages 2628-2645, June.
    12. Alexandar Angelus, 2011. "A Multiechelon Inventory Problem with Secondary Market Sales," Management Science, INFORMS, vol. 57(12), pages 2145-2162, December.
    13. Stephen C. Graves & Tor Schoenmeyr, 2016. "Strategic Safety-Stock Placement in Supply Chains with Capacity Constraints," Manufacturing & Service Operations Management, INFORMS, vol. 18(3), pages 445-460, July.
    14. Qingkai Ji & Lijun Sun & Xiangpei Hu & Jing Hou, 2016. "Optimal policies of a two-echelon serial inventory system with general limited capacities," International Journal of Production Research, Taylor & Francis Journals, vol. 54(20), pages 6142-6155, October.
    15. Rodney P. Parker & Roman Kapuściński, 2011. "Managing a Noncooperative Supply Chain with Limited Capacity," Operations Research, INFORMS, vol. 59(4), pages 866-881, August.
    16. Süleyman Demirel & Izak Duenyas & Roman Kapuscinski, 2015. "Production and Inventory Control for a Make-to-Stock/Calibrate-to-Order System with Dedicated and Shared Resources," Operations Research, INFORMS, vol. 63(4), pages 823-839, August.
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    18. Peter Berling & Victor Martínez‐de‐Albéniz, 2016. "A characterization of optimal base‐stock levels for a multistage serial supply chain," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(1), pages 32-46, February.

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