IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v44y2022i3d10.1007_s10878-020-00538-8.html
   My bibliography  Save this article

An approximation algorithm for stochastic multi-level facility location problem with soft capacities

Author

Listed:
  • Chenchen Wu

    (Tianjin University of Technology)

  • Donglei Du

    (University of New Brunswick)

  • Yue Kang

    (Beijing University of Technology)

Abstract

Facility location problem is one of the most important problems in the combinatorial optimization. The multi-level facility location problem and the facility location with capacities are important variants for the classical facility location problem. In this work, we consider the multilevel facility location problem with soft capacities in the uncertain scenario. The uncertainty setting means the location process is stochastic. We consider a two-stage model. The soft-capacities setting means each facility has multiple capacities by paying multiple opening cost. The multi-level setting means the client needs to connect to a path. We propose a bifactor $$ (1/\alpha ,6/(1-2\alpha ) )$$ ( 1 / α , 6 / ( 1 - 2 α ) ) -approximation algorithm for the stochastic multi-level facility location problem (SMLFLP), where $$ \alpha \in (0,0.5) $$ α ∈ ( 0 , 0.5 ) is a given constant. Then, we reduce the stochastic multi-level facility location problem with soft capacities to SMLFLP. The reduction implies a $$ \left( 1/\alpha + 6/(1-2\alpha ) \right) $$ 1 / α + 6 / ( 1 - 2 α ) -approximation algorithm. The ratio is 14.9282 when setting $$ \alpha = 0.183 $$ α = 0.183 .

Suggested Citation

  • Chenchen Wu & Donglei Du & Yue Kang, 2022. "An approximation algorithm for stochastic multi-level facility location problem with soft capacities," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1680-1692, October.
    • Handle: RePEc:spr:jcomop:v:44:y:2022:i:3:d:10.1007_s10878-020-00538-8
    DOI: 10.1007/s10878-020-00538-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-020-00538-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10878-020-00538-8?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
    ---><---

    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. Min Li & Dachuan Xu & Dongmei Zhang & Tong Zhang, 2019. "A Streaming Algorithm for k-Means with Approximate Coreset," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(01), pages 1-18, February.
    2. Dongmei Zhang & Dachuan Xu & Yishui Wang & Peng Zhang & Zhenning Zhang, 2018. "A local search approximation algorithm for a squared metric k-facility location problem," Journal of Combinatorial Optimization, Springer, vol. 35(4), pages 1168-1184, May.
    3. Lu Han & Dachuan Xu & Donglei Du & Dongmei Zhang, 2018. "A local search approximation algorithm for the uniform capacitated k-facility location problem," Journal of Combinatorial Optimization, Springer, vol. 35(2), pages 409-423, February.
    Full references (including those not matched with items on IDEAS)

    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. Chenchen Wu & Donglei Du & Yue Kang, 0. "An approximation algorithm for stochastic multi-level facility location problem with soft capacities," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-13.
    2. Min Li, 2022. "The bi-criteria seeding algorithms for two variants of k-means problem," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1693-1704, October.
    3. Sai Ji & Dachuan Xu & Min Li & Yishui Wang, 2022. "Approximation algorithms for two variants of correlation clustering problem," Journal of Combinatorial Optimization, Springer, vol. 43(5), pages 933-952, July.
    4. Sai Ji & Dachuan Xu & Min Li & Yishui Wang, 0. "Approximation algorithms for two variants of correlation clustering problem," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-20.

    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:spr:jcomop:v:44:y:2022:i:3:d:10.1007_s10878-020-00538-8. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.