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Matrix-augmentation approach for machine repair problem with generally distributed repair times during working breakdown periods

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  • Wu, Chia-Huang
  • Yang, Dong-Yuh
  • He, Ting-En

Abstract

In the manufacturing industry, production facilities for product manufacturing often contain unreliable operating machines and standbys. The machines can break down and result in productivity loss, and have to be repaired by the repairmen. To evaluate the system performance in operations and production management accurately, a general mathematical model is proposed to investigate the machine repair problem with an unreliable repairman, working breakdowns, and multiple vacations. A novel matrix-augmentation approach is introduced to simplify the analysis process and to derive the stationary distribution of the number of failed machines in the system when the classical supplementary variable technique cannot evolve the steady-state probability recursively. Furthermore, explicit formulas of various performance metrics are developed and numerically computed corresponding to various repair time distributions during working breakdown periods. Finally, an optimization problem with multiple objective functions is formulated with two different objective functions: the expected cost and machine availability. The NSGA-II algorithm is applied to perform numerical experiments and to provide Pareto-efficient solutions for managers and decision-makers.

Suggested Citation

  • Wu, Chia-Huang & Yang, Dong-Yuh & He, Ting-En, 2024. "Matrix-augmentation approach for machine repair problem with generally distributed repair times during working breakdown periods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 225(C), pages 1019-1038.
    • Handle: RePEc:eee:matcom:v:225:y:2024:i:c:p:1019-1038
    DOI: 10.1016/j.matcom.2023.09.026
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    References listed on IDEAS

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    1. Kuo-Hsiung Wang & Cheng-Dar Liou & Ya-Lin Wang, 2014. "Profit optimisation of the multiple-vacation machine repair problem using particle swarm optimisation," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(8), pages 1769-1780, August.
    2. Jau-Chuan Ke & Tzu-Hsin Liu & Ying-Lin Hsu & Hui-Tzu Ku, 2019. "Analysis of machine-repairing systems with server breakdown and delayed repairs," International Journal of Industrial and Systems Engineering, Inderscience Enterprises Ltd, vol. 31(4), pages 517-534.
    3. Haque, Lani & Armstrong, Michael J., 2007. "A survey of the machine interference problem," European Journal of Operational Research, Elsevier, vol. 179(2), pages 469-482, June.
    4. Tao Jiang & Baogui Xin, 2019. "Computational analysis of the queue with working breakdowns and delaying repair under a Bernoulli-schedule-controlled policy," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(4), pages 926-941, February.
    5. Kumar, Pankaj & Jain, Madhu, 2020. "Reliability analysis of a multi-component machining system with service interruption, imperfect coverage, and reboot," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    6. Wu‐Lin Chen, 2018. "System reliability analysis of retrial machine repair systems with warm standbys and a single server of working breakdown and recovery policy," Systems Engineering, John Wiley & Sons, vol. 21(1), pages 59-69, January.
    7. Tseng-Chang Yen & Chia-Huang Wu & Kuo-Hsiung Wang & Wei-Ping Lai, 2022. "Optimisation analysis of the F -policy retrial machine repair problem with working breakdowns," International Journal of Industrial and Systems Engineering, Inderscience Enterprises Ltd, vol. 40(2), pages 200-227.
    8. Meena, Rakesh Kumar & Jain, Madhu & Assad, Assif & Sethi, Rachita & Garg, Deepika, 2022. "Performance and cost comparative analysis for M/G/1 repairable machining system with N-policy vacation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 315-328.
    9. Meena, Rakesh Kumar & Jain, Madhu & Sanga, Sudeep Singh & Assad, Assif, 2019. "Fuzzy modeling and harmony search optimization for machining system with general repair, standby support and vacation," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 858-873.
    10. Yang, Dong-Yuh & Wu, Chia-Huang, 2021. "Evaluation of the availability and reliability of a standby repairable system incorporating imperfect switchovers and working breakdowns," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
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