IDEAS home Printed from https://ideas.repec.org/a/inm/ormoor/v39y2014i2p432-444.html
   My bibliography  Save this article

An Approximate Dynamic-Programming Approach to the Joint Replenishment Problem

Author

Listed:
  • Danny Segev

    () (Department of Statistics, University of Haifa, Haifa 31905, Israel)

Abstract

The main contribution of this paper is to propose a new dynamic-programming approach that (epsilon) -approximates the joint replenishment problem, with stationary demands and holding costs, in its discrete-time finite-horizon setting. Our first and foremost objective is to show that the computation time of classical dynamic-programming algorithms can be improved on by orders of magnitude when one is willing to lose an (epsilon) -factor in optimality. Based on synthesizing ideas such as commodity aggregation, approximate dynamic programming, and a few guessing tricks, we show that one can attain any required degree of accuracy in near-polynomial time.

Suggested Citation

  • Danny Segev, 2014. "An Approximate Dynamic-Programming Approach to the Joint Replenishment Problem," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 432-444, May.
  • Handle: RePEc:inm:ormoor:v:39:y:2014:i:2:p:432-444
    DOI: 10.1287/moor.2013.0611
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/moor.2013.0611
    Download Restriction: no

    References listed on IDEAS

    as
    1. Awi Federgruen & Michal Tzur, 1994. "The Joint Replenishment Problem with Time-Varying Costs and Demands: Efficient, Asymptotic and ε-Optimal Solutions," Operations Research, INFORMS, vol. 42(6), pages 1067-1086, December.
    2. Dev Joneja, 1990. "The Joint Replenishment Problem: New Heuristics and Worst Case Performance Bounds," Operations Research, INFORMS, vol. 38(4), pages 711-723, August.
    3. Daniel Adelman & Diego Klabjan, 2005. "Duality and Existence of Optimal Policies in Generalized Joint Replenishment," Mathematics of Operations Research, INFORMS, vol. 30(1), pages 28-50, February.
    4. BARANY, Imre & VAN ROY, Tony & WOLSEY, Laurence A., 1984. "Uncapacitated lot-sizing: the convex hull of solutions," CORE Discussion Papers RP 605, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Retsef Levi & Robin Roundy & David Shmoys & Maxim Sviridenko, 2008. "A Constant Approximation Algorithm for the One-Warehouse Multiretailer Problem," Management Science, INFORMS, vol. 54(4), pages 763-776, April.
    6. Harvey M. Wagner & Thomson M. Whitin, 1958. "Dynamic Version of the Economic Lot Size Model," Management Science, INFORMS, vol. 5(1), pages 89-96, October.
    7. Arthur F. Veinott, 1969. "Minimum Concave-Cost Solution of Leontief Substitution Models of Multi-Facility Inventory Systems," Operations Research, INFORMS, vol. 17(2), pages 262-291, April.
    8. Willard I. Zangwill, 1966. "A Deterministic Multiproduct, Multi-Facility Production and Inventory Model," Operations Research, INFORMS, vol. 14(3), pages 486-507, June.
    9. Chung-Piaw Teo & Dimitris Bertsimas, 2001. "Multistage Lot Sizing Problems via Randomized Rounding," Operations Research, INFORMS, vol. 49(4), pages 599-608, August.
    10. Retsef Levi & Robin O. Roundy & David B. Shmoys, 2006. "Primal-Dual Algorithms for Deterministic Inventory Problems," Mathematics of Operations Research, INFORMS, vol. 31(2), pages 267-284, May.
    Full references (including those not matched with items on IDEAS)

    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:inm:ormoor:v:39:y:2014:i:2:p:432-444. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Matthew Walls). General contact details of provider: http://edirc.repec.org/data/inforea.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.