IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v224y2015i1p25-5010.1007-s10479-012-1131-4.html
   My bibliography  Save this article

The stochastic opportunistic replacement problem, part I: models incorporating individual component lives

Author

Listed:
  • Michael Patriksson
  • Ann-Brith Strömberg
  • Adam Wojciechowski

Abstract

We consider an extension of the opportunistic replacement problem, which has been studied by Dickman et al. (The Journal of the Operational Research Society of India, 28:165–175, 1991 ), Andréasson (Optimization of opportunistic replacement activities in deterministic and stochastic multi-component systems, Licentiate thesis, Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Göteborg, Sweden, 2004 ), and Almgren et al. (The opportunistic replacement problem: analysis and case studies, Preprint, Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Göteborg, Sweden, 2011 ), that allows the individuals of the same component to have non-identical lives. Formulating and solving this problem constitute a first step towards solving the opportunistic replacement problem with uncertain component lives. We show that the problem is NP-hard even with time independent costs, and present two 0–1 integer programming models for the problem. We show that in model I the integrality requirement on a majority of the variables can be relaxed; this is in contrast to model II and the model from Andréasson (Optimization of opportunistic replacement activities in deterministic and stochastic multi-component systems, Licentiate thesis, Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Göteborg, Sweden, 2004 ). We remove all superfluous variables and constraints in model I and show that the remaining constraints are facet inducing. We also utilize a linear transformation of model I to obtain a stronger version of model II, i.e., model II + , which inherits the polyhedral properties of model I. Numerical experiments show that the solution time of model I is significantly lower than those of both model II and Andréasson’s model. It is also slightly lower than the solution time of model II + . Copyright Springer Science+Business Media, LLC 2015

Suggested Citation

  • Michael Patriksson & Ann-Brith Strömberg & Adam Wojciechowski, 2015. "The stochastic opportunistic replacement problem, part I: models incorporating individual component lives," Annals of Operations Research, Springer, vol. 224(1), pages 25-50, January.
    • Handle: RePEc:spr:annopr:v:224:y:2015:i:1:p:25-50:10.1007/s10479-012-1131-4
    DOI: 10.1007/s10479-012-1131-4
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-012-1131-4
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-012-1131-4?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.

    Citations

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


    Cited by:

    1. Efraim Laksman & Ann-Brith Strömberg & Michael Patriksson, 2020. "The stochastic opportunistic replacement problem, part III: improved bounding procedures," Annals of Operations Research, Springer, vol. 292(2), pages 711-733, September.

    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:annopr:v:224:y:2015:i:1:p:25-50:10.1007/s10479-012-1131-4. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.