IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v76y2012i3p289-319.html
   My bibliography  Save this article

The opportunistic replacement problem: theoretical analyses and numerical tests

Author

Listed:
  • Torgny Almgren
  • Niclas Andréasson
  • Michael Patriksson
  • Ann-Brith Strömberg
  • Adam Wojciechowski
  • Magnus Önnheim

Abstract

We consider a model for determining optimal opportunistic maintenance schedules w.r.t. a maximum replacement interval. This problem generalizes that of Dickman et al. (J Oper Res Soc India 28:165–175, 1991 ) and is a natural starting point for modelling replacement schedules of more complex systems. We show that this basic opportunistic replacement problem is NP-hard, that the convex hull of the set of feasible replacement schedules is full-dimensional, that all the inequalities of the model are facet-inducing, and present a new class of facets obtained through a $${\{0, \frac{1}{2}\}}$$ -Chvátal–Gomory rounding. For costs monotone with time, a class of elimination constraints is introduced to reduce the computation time; it allows maintenance only when the replacement of at least one component is necessary. For costs decreasing with time, these constraints eliminate non-optimal solutions. When maintenance occasions are fixed, the remaining problem is stated as a linear program and solved by a greedy procedure. Results from a case study on aircraft engine maintenance illustrate the advantage of the optimization model over simpler policies. We include the new class of facets in a branch-and-cut framework and note a decrease in the number of branch-and-bound nodes and simplex iterations for most instance classes with time dependent costs. For instance classes with time independent costs and few components the elimination constraints are used favorably. For fixed maintenance occasions the greedy procedure reduces the computation time as compared with linear programming techniques for all instances tested. Copyright Springer-Verlag 2012

Suggested Citation

  • Torgny Almgren & Niclas Andréasson & Michael Patriksson & Ann-Brith Strömberg & Adam Wojciechowski & Magnus Önnheim, 2012. "The opportunistic replacement problem: theoretical analyses and numerical tests," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(3), pages 289-319, December.
    • Handle: RePEc:spr:mathme:v:76:y:2012:i:3:p:289-319
    DOI: 10.1007/s00186-012-0400-y
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00186-012-0400-y
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00186-012-0400-y?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. Robin P. Nicolai & Rommert Dekker, 2008. "Optimal Maintenance of Multi-component Systems: A Review," Springer Series in Reliability Engineering, in: Complex System Maintenance Handbook, chapter 11, pages 263-286, Springer.
    2. Rommert Dekker & Ralph Wildeman & Frank Duyn Schouten, 1997. "A review of multi-component maintenance models with economic dependence," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 45(3), pages 411-435, October.
    3. Pintelon, L. M. & Gelders, L. F., 1992. "Maintenance management decision making," European Journal of Operational Research, Elsevier, vol. 58(3), pages 301-317, May.
    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. 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.

    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. Ayse Sena Eruguz & Tarkan Tan & Geert‐Jan van Houtum, 2017. "Optimizing usage and maintenance decisions for k‐out‐of‐n systems of moving assets," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(5), pages 418-434, August.
    2. Nguyen, Ho Si Hung & Do, Phuc & Vu, Hai-Canh & Iung, Benoit, 2019. "Dynamic maintenance grouping and routing for geographically dispersed production systems," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 392-404.
    3. Zhicheng Zhu & Yisha Xiang & Bo Zeng, 2021. "Multicomponent Maintenance Optimization: A Stochastic Programming Approach," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 898-914, July.
    4. Lu, Biao & Zhou, Xiaojun, 2017. "Opportunistic preventive maintenance scheduling for serial-parallel multistage manufacturing systems with multiple streams of deterioration," Reliability Engineering and System Safety, Elsevier, vol. 168(C), pages 116-127.
    5. Kivanç, İpek & Fecarotti, Claudia & Raassens, Néomie & van Houtum, Geert-Jan, 2024. "A scalable multi-objective maintenance optimization model for systems with multiple heterogeneous components and a finite lifespan," European Journal of Operational Research, Elsevier, vol. 315(2), pages 567-579.
    6. Briš, Radim & Byczanski, Petr & Goňo, Radomír & Rusek, Stanislav, 2017. "Discrete maintenance optimization of complex multi-component systems," Reliability Engineering and System Safety, Elsevier, vol. 168(C), pages 80-89.
    7. Markus Bohlin & Mathias Wärja, 2015. "Maintenance optimization with duration-dependent costs," Annals of Operations Research, Springer, vol. 224(1), pages 1-23, January.
    8. Zhu, Mixin & Zhou, Xiaojun, 2023. "Hierarchical-clustering-based joint optimization of spare part provision and maintenance scheduling for serial-parallel multi-station manufacturing systems," International Journal of Production Economics, Elsevier, vol. 264(C).
    9. Jyrki Savolainen & Michele Urbani, 2021. "Maintenance optimization for a multi-unit system with digital twin simulation," Journal of Intelligent Manufacturing, Springer, vol. 32(7), pages 1953-1973, October.
    10. Maaroufi, Ghofrane & Chelbi, Anis & Rezg, Nidhal, 2013. "Optimal selective renewal policy for systems subject to propagated failures with global effect and failure isolation phenomena," Reliability Engineering and System Safety, Elsevier, vol. 114(C), pages 61-70.
    11. Linnéusson, Gary & Ng, Amos H.C. & Aslam, Tehseen, 2020. "A hybrid simulation-based optimization framework supporting strategic maintenance development to improve production performance," European Journal of Operational Research, Elsevier, vol. 281(2), pages 402-414.
    12. Hashemi, M. & Asadi, M. & Tavangar, M., 2022. "Optimal maintenance strategies for coherent systems: A warranty dependent approach," Reliability Engineering and System Safety, Elsevier, vol. 217(C).
    13. Petchrompo, Sanyapong & Parlikad, Ajith Kumar, 2019. "A review of asset management literature on multi-asset systems," Reliability Engineering and System Safety, Elsevier, vol. 181(C), pages 181-201.
    14. Safaei, Fatemeh & Châtelet, Eric & Ahmadi, Jafar, 2020. "Optimal age replacement policy for parallel and series systems with dependent components," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    15. Vu, Hai Canh & Do, Phuc & Fouladirad, Mitra & Grall, Antoine, 2020. "Dynamic opportunistic maintenance planning for multi-component redundant systems with various types of opportunities," Reliability Engineering and System Safety, Elsevier, vol. 198(C).
    16. Zhu, Wenjin & Fouladirad, Mitra & Bérenguer, Christophe, 2016. "A multi-level maintenance policy for a multi-component and multifailure mode system with two independent failure modes," Reliability Engineering and System Safety, Elsevier, vol. 153(C), pages 50-63.
    17. Tazi, Nacef & Châtelet, Eric & Bouzidi, Youcef, 2018. "How combined performance and propagation of failure dependencies affect the reliability of a MSS," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 531-541.
    18. Jaturonnatee, J. & Murthy, D.N.P. & Boondiskulchok, R., 2006. "Optimal preventive maintenance of leased equipment with corrective minimal repairs," European Journal of Operational Research, Elsevier, vol. 174(1), pages 201-215, October.
    19. de Jonge, Bram & Klingenberg, Warse & Teunter, Ruud & Tinga, Tiedo, 2016. "Reducing costs by clustering maintenance activities for multiple critical units," Reliability Engineering and System Safety, Elsevier, vol. 145(C), pages 93-103.
    20. Zhang, Xiaohong & Zeng, Jianchao, 2017. "Joint optimization of condition-based opportunistic maintenance and spare parts provisioning policy in multiunit systems," European Journal of Operational Research, Elsevier, vol. 262(2), pages 479-498.

    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:mathme:v:76:y:2012:i:3:p:289-319. 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.