IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v63y2016i1p32-46.html
   My bibliography  Save this article

A characterization of optimal base‐stock levels for a multistage serial supply chain

Author

Listed:
  • Peter Berling
  • Victor Martínez‐de‐Albéniz

Abstract

In this article, we present a multistage model to optimize inventory control decisions under stochastic demand and continuous review. We first formulate the general problem for continuous stages and use a decomposition solution approach: since it is never optimal to let orders cross, the general problem can be broken into a set of single‐unit subproblems that can be solved in a sequential fashion. These subproblems are optimal control problems for which a differential equation must be solved. This can be done easily by recursively identifying coefficients and performing a line search. The methodology is then extended to a discrete number of stages and allows us to compute the optimal solution in an efficient manner, with a competitive complexity. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 32–46, 2016

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:63:y:2016:i:1:p:32-46
    DOI: 10.1002/nav.21675
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.21675
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.21675?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Kevin H. Shang & Jing-Sheng Song, 2003. "Newsvendor Bounds and Heuristic for Optimal Policies in Serial Supply Chains," Management Science, INFORMS, vol. 49(5), pages 618-638, May.
    2. Peter Berling & Victor Martínez-de-Albéniz, 2011. "Optimal Inventory Policies when Purchase Price and Demand Are Stochastic," Operations Research, INFORMS, vol. 59(1), pages 109-124, February.
    3. Stephen C. Graves, 1985. "A Multi-Echelon Inventory Model for a Repairable Item with One-for-One Replenishment," Management Science, INFORMS, vol. 31(10), pages 1247-1256, October.
    4. Fangruo Chen & Jing-Sheng Song, 2001. "Optimal Policies for Multiechelon Inventory Problems with Markov-Modulated Demand," Operations Research, INFORMS, vol. 49(2), pages 226-234, April.
    5. Awi Federgruen & Paul Zipkin, 1984. "Computational Issues in an Infinite-Horizon, Multiechelon Inventory Model," Operations Research, INFORMS, vol. 32(4), pages 818-836, August.
    6. Kaj Rosling, 1989. "Optimal Inventory Policies for Assembly Systems Under Random Demands," Operations Research, INFORMS, vol. 37(4), pages 565-579, August.
    7. 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.
    8. Minner, Stefan, 2003. "Multiple-supplier inventory models in supply chain management: A review," International Journal of Production Economics, Elsevier, vol. 81(1), pages 265-279, January.
    9. Gregory DeCroix & Jing-Sheng Song & Paul Zipkin, 2005. "A Series System with Returns: Stationary Analysis," Operations Research, INFORMS, vol. 53(2), pages 350-362, April.
    10. Sven Axsäter & Kaj Rosling, 1993. "Notes: Installation vs. Echelon Stock Policies for Multilevel Inventory Control," Management Science, INFORMS, vol. 39(10), pages 1274-1280, October.
    11. Fangruo Chen, 1998. "Echelon Reorder Points, Installation Reorder Points, and the Value of Centralized Demand Information," Management Science, INFORMS, vol. 44(12-Part-2), pages 221-234, December.
    12. David G. Lawson & Evan L. Porteus, 2000. "Multistage Inventory Management with Expediting," Operations Research, INFORMS, vol. 48(6), pages 878-893, December.
    13. Alp Muharremoglu & John N. Tsitsiklis, 2008. "A Single-Unit Decomposition Approach to Multiechelon Inventory Systems," Operations Research, INFORMS, vol. 56(5), pages 1089-1103, October.
    14. 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.
    15. Guillermo Gallego & Paul Zipkin, 1999. "Stock Positioning and Performance Estimation in Serial Production-Transportation Systems," Manufacturing & Service Operations Management, INFORMS, vol. 1(1), pages 77-88.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Svoboda, Josef & Minner, Stefan & Yao, Man, 2021. "Typology and literature review on multiple supplier inventory control models," European Journal of Operational Research, Elsevier, vol. 293(1), pages 1-23.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Peter Berling & Victor Martínez-de-Albéniz, 2016. "Dynamic Speed Optimization in Supply Chains with Stochastic Demand," Transportation Science, INFORMS, vol. 50(3), pages 1114-1127, August.
    3. Lingxiu Dong & Hau L. Lee, 2003. "Optimal Policies and Approximations for a Serial Multiechelon Inventory System with Time-Correlated Demand," Operations Research, INFORMS, vol. 51(6), pages 969-980, December.
    4. 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.
    5. Retsef Levi & Robin Roundy & Van Anh Truong & Xinshang Wang, 2017. "Provably Near-Optimal Balancing Policies for Multi-Echelon Stochastic Inventory Control Models," Mathematics of Operations Research, INFORMS, vol. 42(1), pages 256-276, January.
    6. Alexandar Angelus, 2011. "A Multiechelon Inventory Problem with Secondary Market Sales," Management Science, INFORMS, vol. 57(12), pages 2145-2162, December.
    7. 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.
    8. Rodney P. Parker & Roman Kapuscinski, 2004. "Optimal Policies for a Capacitated Two-Echelon Inventory System," Operations Research, INFORMS, vol. 52(5), pages 739-755, October.
    9. Vanteddu, Gangaraju & Chinnam, Ratna Babu & Gushikin, Oleg, 2011. "Supply chain focus dependent supplier selection problem," International Journal of Production Economics, Elsevier, vol. 129(1), pages 204-216, January.
    10. Ming Hu & Yi Yang, 2014. "Modified Echelon ( r, Q ) Policies with Guaranteed Performance Bounds for Stochastic Serial Inventory Systems," Operations Research, INFORMS, vol. 62(4), pages 812-828, August.
    11. Alp Muharremoglu & John N. Tsitsiklis, 2008. "A Single-Unit Decomposition Approach to Multiechelon Inventory Systems," Operations Research, INFORMS, vol. 56(5), pages 1089-1103, October.
    12. Guillermo Gallego & Özalp Özer, 2003. "Optimal Replenishment Policies for Multiechelon Inventory Problems Under Advance Demand Information," Manufacturing & Service Operations Management, INFORMS, vol. 5(2), pages 157-175, February.
    13. 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.
    14. Johan Marklund, 2002. "Centralized inventory control in a two‐level distribution system with Poisson demand," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(8), pages 798-822, December.
    15. Diwakar Gupta & N. Selvaraju, 2006. "Performance Evaluation and Stock Allocation in Capacitated Serial Supply Systems," Manufacturing & Service Operations Management, INFORMS, vol. 8(2), pages 169-191, July.
    16. Geert-Jan van Houtum & Alan Scheller-Wolf & Jinxin Yi, 2007. "Optimal Control of Serial Inventory Systems with Fixed Replenishment Intervals," Operations Research, INFORMS, vol. 55(4), pages 674-687, August.
    17. Jing-Sheng Song & Paul Zipkin, 2013. "Supply Streams," Manufacturing & Service Operations Management, INFORMS, vol. 15(3), pages 444-457, July.
    18. 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.
    19. Warsing, Donald P. & Wangwatcharakul, Worawut & King, Russell E., 2019. "Computing base-stock levels for a two-stage supply chain with uncertain supply," Omega, Elsevier, vol. 89(C), pages 92-109.
    20. Guillermo Gallego & Özalp Özer & Paul Zipkin, 2007. "Bounds, Heuristics, and Approximations for Distribution Systems," Operations Research, INFORMS, vol. 55(3), pages 503-517, June.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:navres:v:63:y:2016:i:1:p:32-46. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.