IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v250y2016i1p155-163.html
   My bibliography  Save this article

Constant approximation algorithms for the one warehouse multiple retailers problem with backlog or lost-sales

Author

Listed:
  • Gayon, J.-P.
  • Massonnet, G.
  • Rapine, C.
  • Stauffer, G.

Abstract

We consider the One Warehouse Multi-Retailer (OWMR) problem with deterministic time-varying demand in the case where shortages are allowed. Demand may be either backlogged or lost. We present a simple combinatorial algorithm to build an approximate solution from a decomposition of the system into single-echelon subproblems. We establish that the algorithm has a performance guarantee of 3 for the OWMR with backlog under mild assumptions on the cost structure. In addition, we improve this guarantee to 2 in the special case of the Joint-Replenishment Problem (JRP) with backlog. As a by-product of our approach, we show that our decomposition provides a new lower bound of the optimal cost. A similar technique also leads to a 2-approximation for the OWMR problem with lost-sales. In all cases, the complexity of the algorithm is linear in the number of retailers and quadratic in the number of time periods, which makes it a valuable tool for practical applications. To the best of our knowledge, these are the first constant approximations for the OWMR with shortages.

Suggested Citation

  • Gayon, J.-P. & Massonnet, G. & Rapine, C. & Stauffer, G., 2016. "Constant approximation algorithms for the one warehouse multiple retailers problem with backlog or lost-sales," European Journal of Operational Research, Elsevier, vol. 250(1), pages 155-163.
  • Handle: RePEc:eee:ejores:v:250:y:2016:i:1:p:155-163
    DOI: 10.1016/j.ejor.2015.10.054
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221715009807
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Absi, Nabil & Kedad-Sidhoum, Safia, 2008. "The multi-item capacitated lot-sizing problem with setup times and shortage costs," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1351-1374, March.
    2. 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.
    3. Aksen, Deniz & Altinkemer, Kemal & Chand, Suresh, 2003. "The single-item lot-sizing problem with immediate lost sales," European Journal of Operational Research, Elsevier, vol. 147(3), pages 558-566, June.
    4. Willard I. Zangwill, 1966. "A Deterministic Multi-Period Production Scheduling Model with Backlogging," Management Science, INFORMS, vol. 13(1), pages 105-119, September.
    5. 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.
    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. repec:spr:mathme:v:88:y:2018:i:3:d:10.1007_s00186-018-0642-4 is not listed 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:eee:ejores:v:250:y:2016:i:1:p:155-163. 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: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.