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An exact algorithm for the reliability redundancy allocation problem

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  • Caserta, Marco
  • Voß, Stefan

Abstract

The redundancy allocation problem is the problem of finding an optimal allocation of redundant components subject to a set of resource constraints. The problem studied in this paper refers to a series-parallel system configuration and allows for component mixing. We propose a new modeling/solution approach, in which the problem is transformed into a multiple choice knapsack problem and solved to optimality via a branch and cut algorithm. The algorithm is tested on well-known sets of benchmark instances. All instances have been solved to optimality in milliseconds or very few seconds on a normal workstation.

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  • Caserta, Marco & Voß, Stefan, 2015. "An exact algorithm for the reliability redundancy allocation problem," European Journal of Operational Research, Elsevier, vol. 244(1), pages 110-116.
    • Handle: RePEc:eee:ejores:v:244:y:2015:i:1:p:110-116
    DOI: 10.1016/j.ejor.2015.01.008
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    References listed on IDEAS

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    1. Cao, Dingzhou & Murat, Alper & Chinnam, Ratna Babu, 2013. "Efficient exact optimization of multi-objective redundancy allocation problems in series-parallel systems," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 154-163.
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    5. Liang, Yun-Chia & Chen, Yi-Ching, 2007. "Redundancy allocation of series-parallel systems using a variable neighborhood search algorithm," Reliability Engineering and System Safety, Elsevier, vol. 92(3), pages 323-331.
    6. Sadjadi, Seyed Jafar & Soltani, R., 2009. "An efficient heuristic versus a robust hybrid meta-heuristic for general framework of serial–parallel redundancy problem," Reliability Engineering and System Safety, Elsevier, vol. 94(11), pages 1703-1710.
    7. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2014. "Cold vs. hot standby mission operation cost minimization for 1-out-of-N systems," European Journal of Operational Research, Elsevier, vol. 234(1), pages 155-162.
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    Cited by:

    1. Huang, Xianzhen & Coolen, Frank P.A. & Coolen-Maturi, Tahani, 2019. "A heuristic survival signature based approach for reliability-redundancy allocation," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 511-517.
    2. Young Woong Park, 2020. "MILP Models for Complex System Reliability Redundancy Allocation with Mixed Components," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 600-619, July.
    3. Behzad Karimi & Seyed Taghi Akhavan Niaki & Seyyed Masih Miriha & Mahsa Ghare Hasanluo & Shima Javanmard, 2019. "A weighted K-means clustering approach to solve the redundancy allocation problem of systems having components with different failures," Journal of Risk and Reliability, , vol. 233(6), pages 925-942, December.
    4. Diallo, Claver & Venkatadri, Uday & Khatab, Abdelhakim & Liu, Zhuojun, 2018. "Optimal selective maintenance decisions for large serial k-out-of-n: G systems under imperfect maintenance," Reliability Engineering and System Safety, Elsevier, vol. 175(C), pages 234-245.
    5. Enrico Zio & Hadi Gholinezhad, 2023. "Redundancy Allocation of Components with Time-Dependent Failure Rates," Mathematics, MDPI, vol. 11(16), pages 1-27, August.
    6. Li, Yan-Fu & Zhang, Hanxiao, 2022. "The methods for exactly solving redundancy allocation optimization for multi-state series–parallel systems," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    7. Pradip Kundu, 2021. "A multi-objective reliability-redundancy allocation problem with active redundancy and interval type-2 fuzzy parameters," Operational Research, Springer, vol. 21(4), pages 2433-2458, December.
    8. de Paula, Cassio Pereira & Visnadi, Lais Bittencourt & de Castro, Helio Fiori, 2019. "Multi-objective optimization in redundant system considering load sharing," Reliability Engineering and System Safety, Elsevier, vol. 181(C), pages 17-27.
    9. Debasis Bhattacharya & Soma Roychowdhury, 2017. "A redundancy strategy for minimizing cost in systems with non-disjoint subsystems under reliability constraint," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(2), pages 645-655, November.
    10. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2018. "Heterogeneous standby systems with shocks-driven preventive replacements," European Journal of Operational Research, Elsevier, vol. 266(3), pages 1189-1197.
    11. Caserta, Marco & Voß, Stefan, 2019. "The robust multiple-choice multidimensional knapsack problem," Omega, Elsevier, vol. 86(C), pages 16-27.
    12. Yuxiong Li & Xianzhen Huang & Xinong En & Pengfei Ding, 2019. "A New System Reliability Optimization Model Based on Swapping Existing Components," Complexity, Hindawi, vol. 2019, pages 1-14, November.
    13. Xu, Dong & Tian, Yubin & Shi, Junbiao & Wang, Dianpeng & Zhang, Ming & Li, Haijin, 2023. "Reliability analysis and optimal redundancy for a satellite power supply system based on a new dynamic k-out-of-n: G model," Reliability Engineering and System Safety, Elsevier, vol. 236(C).
    14. Jiangbin Zhao & Shubin Si & Zhiqiang Cai & Ming Su & Wei Wang, 2019. "Multiobjective optimization of reliability–redundancy allocation problems for serial parallel-series systems based on importance measure," Journal of Risk and Reliability, , vol. 233(5), pages 881-897, October.
    15. Toppila, Antti & Salo, Ahti, 2017. "Selection of risk reduction portfolios under interval-valued probabilities," Reliability Engineering and System Safety, Elsevier, vol. 163(C), pages 69-78.
    16. Liping Ge & Stefan Voß & Lin Xie, 2022. "Robustness and disturbances in public transport," Public Transport, Springer, vol. 14(1), pages 191-261, March.
    17. Reihaneh, Mohammad & Abouei Ardakan, Mostafa & Eskandarpour, Majid, 2022. "An exact algorithm for the redundancy allocation problem with heterogeneous components under the mixed redundancy strategy," European Journal of Operational Research, Elsevier, vol. 297(3), pages 1112-1125.
    18. Zhang, Zixuan & Yang, Lin & Xu, Youwei & Zhu, Ran & Cao, Yining, 2023. "A novel reliability redundancy allocation problem formulation for complex systems," Reliability Engineering and System Safety, Elsevier, vol. 239(C).
    19. Mohamed Arezki Mellal & Enrico Zio, 2019. "An adaptive particle swarm optimization method for multi-objective system reliability optimization," Journal of Risk and Reliability, , vol. 233(6), pages 990-1001, December.
    20. Muhuri, Pranab K. & Nath, Rahul, 2019. "A novel evolutionary algorithmic solution approach for bilevel reliability-redundancy allocation problem," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    21. Levitin, Gregory & Finkelstein, Maxim & Li, Yan-Feng, 2020. "Balancing mission success probability and risk of system loss by allocating redundancy in systems operating with a rescue option," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    22. Yeh, Wei-Chang, 2022. "BAT-based algorithm for finding all Pareto solutions of the series-parallel redundancy allocation problem with mixed components," Reliability Engineering and System Safety, Elsevier, vol. 228(C).
    23. Zhao, Peng & Zhang, Yiying & Chen, Jianbin, 2017. "Optimal allocation policy of one redundancy in a n-component series system," European Journal of Operational Research, Elsevier, vol. 257(2), pages 656-668.
    24. Jaeyoung Yang & Yong-Hyuk Kim & Yourim Yoon, 2022. "A Memetic Algorithm with a Novel Repair Heuristic for the Multiple-Choice Multidimensional Knapsack Problem," Mathematics, MDPI, vol. 10(4), pages 1-15, February.

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