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The stochastic opportunistic replacement problem, part III: improved bounding procedures

Author

Listed:
  • Efraim Laksman

    (Chalmers University of Technology and University of Gothenburg)

  • Ann-Brith Strömberg

    (Chalmers University of Technology and University of Gothenburg)

  • Michael Patriksson

    (Chalmers University of Technology and University of Gothenburg)

Abstract

We consider the problem to find a schedule for component replacement in a multi-component system, whose components possess stochastic lives and economic dependencies, such that the expected costs for maintenance during a pre-defined time period are minimized. The problem was considered in Patriksson et al. (Ann Oper Res 224:51–75, 2015b), in which a two-stage approximation of the problem was optimized through decomposition (denoted the optimization policy). The current paper improves the effectiveness of the decomposition approach by establishing a tighter bound on the value of the recourse function (i.e., the second stage in the approximation). A general lower bound on the expected maintenance cost is also established. Numerical experiments with 100 simulation scenarios for each of four test instances show that the tighter bound yields a decomposition generating fewer optimality cuts. They also illustrate the quality of the lower bound. Contrary to results presented earlier, an age-based policy performs on par with the optimization policy, although most simple policies perform worse than the optimization policy.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:292:y:2020:i:2:d:10.1007_s10479-019-03278-z
    DOI: 10.1007/s10479-019-03278-z
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    References listed on IDEAS

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    1. Aghezzaf, El-Houssaine & Khatab, Abdelhakim & Tam, Phuoc Le, 2016. "Optimizing production and imperfect preventive maintenance planning׳s integration in failure-prone manufacturing systems," Reliability Engineering and System Safety, Elsevier, vol. 145(C), pages 190-198.
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    3. Wang, Wenbin, 2012. "A stochastic model for joint spare parts inventory and planned maintenance optimisation," European Journal of Operational Research, Elsevier, vol. 216(1), pages 127-139.
    4. 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.
    5. Do, Phuc & Voisin, Alexandre & Levrat, Eric & Iung, Benoit, 2015. "A proactive condition-based maintenance strategy with both perfect and imperfect maintenance actions," Reliability Engineering and System Safety, Elsevier, vol. 133(C), pages 22-32.
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    7. Michael Patriksson & Ann-Brith Strömberg & Adam Wojciechowski, 2015. "The stochastic opportunistic replacement problem, part II: a two-stage solution approach," Annals of Operations Research, Springer, vol. 224(1), pages 51-75, January.
    8. Rasmekomen, Nipat & Parlikad, Ajith Kumar, 2016. "Condition-based maintenance of multi-component systems with degradation state-rate interactions," Reliability Engineering and System Safety, Elsevier, vol. 148(C), pages 1-10.
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    10. 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.
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