IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v49y2002i3p288-302.html
   My bibliography  Save this article

A branch and bound algorithm for computing optimal replacement policies in consecutive k‐out‐of‐n‐systems

Author

Listed:
  • James Flynn
  • Chia‐Shin Chung

Abstract

This paper presents a branch and bound algorithm for computing optimal replacement policies in a discrete‐time, infinite‐horizon, dynamic programming model of a binary coherent system with n statistically independent components, and then specializes the algorithm to consecutive k‐out‐of‐n systems. The objective is to minimize the long‐run expected average undiscounted cost per period. (Costs arise when the system fails and when failed components are replaced.) An earlier paper established the optimality of following a critical component policy (CCP), i.e., a policy specified by a critical component set and the rule: Replace a component if and only if it is failed and in the critical component set. Computing an optimal CCP is a optimization problem with n binary variables and a nonlinear objective function. Our branch and bound algorithm for solving this problem has memory storage requirement O(n) for consecutive k‐out‐of‐n systems. Extensive computational experiments on such systems involving over 350,000 test problems with n ranging from 10 to 150 find this algorithm to be effective when n ≤ 40 or k is near n. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 288–302, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10017

Suggested Citation

  • James Flynn & Chia‐Shin Chung, 2002. "A branch and bound algorithm for computing optimal replacement policies in consecutive k‐out‐of‐n‐systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(3), pages 288-302, April.
    • Handle: RePEc:wly:navres:v:49:y:2002:i:3:p:288-302
    DOI: 10.1002/nav.10017
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.10017
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.10017?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
    ---><---

    References listed on IDEAS

    as
    1. Chia‐Shin Chung & James Flynn, 1997. "A heuristic algorithm for determining replacement policies in k‐out‐of‐n systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(3), pages 273-286, April.
    2. Chia-Shin Chung & James Flynn, 1995. "A Branch-and-Bound Algorithm for Computing Optimal Replacement Policies in K -Out-of- N Systems," Operations Research, INFORMS, vol. 43(5), pages 826-837, October.
    3. William P. Pierskalla & John A. Voelker, 1976. "A survey of maintenance models: The control and surveillance of deteriorating systems," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 23(3), pages 353-388, September.
    4. Y. S. Sherif & M. L. Smith, 1981. "Optimal maintenance models for systems subject to failure–A Review," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 28(1), pages 47-74, March.
    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. Rommert Dekker & Eric Smeitink, 1994. "Preventive maintenance at opportunities of restricted duration," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(3), pages 335-353, April.
    2. Wallace J. Hopp & Suresh K. Nair, 1991. "Timing replacement decisions under discontinuous technological change," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(2), pages 203-220, April.
    3. David T. Abdul‐Malak & Jeffrey P. Kharoufeh & Lisa M. Maillart, 2019. "Maintaining systems with heterogeneous spare parts," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(6), pages 485-501, September.
    4. Pinciroli, Luca & Baraldi, Piero & Zio, Enrico, 2023. "Maintenance optimization in industry 4.0," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    5. Wallace J. Hopp & Sung‐Chi Wu, 1988. "Multiaction maintenance under markovian deterioration and incomplete state information," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(5), pages 447-462, October.
    6. Dmitry BANNIKOV & Nina SIRINA & Alexander SMOLYANINOV, 2018. "Model Of The Maintenance And Repair System In Service Maintenance Management," Transport Problems, Silesian University of Technology, Faculty of Transport, vol. 13(3), pages 5-14, September.
    7. Wang, Wei & Wu, Zhiying & Xiong, Junlin & Xu, Yaofeng, 2018. "Redundancy optimization of cold-standby systems under periodic inspection and maintenance," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 394-402.
    8. Wallace J. Hopp & Yar‐Lin Kuo, 1998. "Heuristics for multicomponent joint replacement: Applications to aircraft engine maintenance," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(5), pages 435-458, August.
    9. Lisa M. Maillart & Xiang Fang, 2006. "Optimal maintenance policies for serial, multi‐machine systems with non‐instantaneous repairs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(8), pages 804-813, December.
    10. Chia‐Shin Chung & James Flynn, 1997. "A heuristic algorithm for determining replacement policies in k‐out‐of‐n systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(3), pages 273-286, April.
    11. David L. Kaufman & Mark E. Lewis, 2007. "Machine maintenance with workload considerations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(7), pages 750-766, October.
    12. Alireza Sabouri & Woonghee Tim Huh & Steven M. Shechter, 2017. "Screening Strategies for Patients on the Kidney Transplant Waiting List," Operations Research, INFORMS, vol. 65(5), pages 1131-1146, October.
    13. Yeek-Hyun Kim & Lyn Thomas, 2013. "Training and repair policies for stand-by systems," Annals of Operations Research, Springer, vol. 208(1), pages 469-487, September.
    14. Retsef Levi & Thomas Magnanti & Yaron Shaposhnik, 2019. "Scheduling with Testing," Management Science, INFORMS, vol. 65(2), pages 776-793, February.
    15. V. Jayabalan & Dipak Chaudhuri, 1992. "Optimal maintenance and replacement policy for a deteriorating system with increased mean downtime," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(1), pages 67-78, February.
    16. Yuri Merizalde & Luis Hernández-Callejo & Oscar Duque-Perez & Víctor Alonso-Gómez, 2019. "Maintenance Models Applied to Wind Turbines. A Comprehensive Overview," Energies, MDPI, vol. 12(2), pages 1-41, January.
    17. Steven M. Shechter & Matthew D. Bailey & Andrew J. Schaefer, 2008. "Replacing nonidentical vital components to extend system life," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(7), pages 700-703, October.
    18. Kut C. So, 1992. "Optimality of control limit policies in replacement models," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(5), pages 685-697, August.
    19. Ian M. Dobbs, 2004. "Replacement Investment: Optimal Economic Life Under Uncertainty," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 31(5‐6), pages 729-757, June.
    20. Schouten, Thijs Nicolaas & Dekker, Rommert & Hekimoğlu, Mustafa & Eruguz, Ayse Sena, 2022. "Maintenance optimization for a single wind turbine component under time-varying costs," European Journal of Operational Research, Elsevier, vol. 300(3), pages 979-991.

    More about this item

    Statistics

    Access and download statistics

    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:wly:navres:v:49:y:2002:i:3:p:288-302. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.