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Fuzzy modeling and harmony search optimization for machining system with general repair, standby support and vacation

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  • Meena, Rakesh Kumar
  • Jain, Madhu
  • Sanga, Sudeep Singh
  • Assad, Assif

Abstract

The queueing analysis of a multi-component machine repair system comprising of operating as well as standby machines and a skilled repairman has been investigated. The server may go for the vacation of random length when there are no failed machines queueing up for the repair job. By taking the remaining repair time as a supplementary variable, the steady state queue size distribution of the number of failed machines in the system is established. Laplace–Stieltjes transform, recursive and supplementary variable approaches are used to derive various system indices such as mean queue length, machine availability, system availability, and operative utilization, etc. To deal with a realistic scenario, the machine repair model is transformed from crisp to fuzzy environment by considering the system parameters corresponding to failure, repair and vacation rates as fuzzy numbers. The numerical illustration and practical application of a flexible manufacturing system for specific repair distributions are presented to visualize the effects of the system parameters on various performance indices. To explore the practical utility of the investigated model, the cost function is framed and cost optimization problem has been analyzed by using Harmony search approach.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:361:y:2019:i:c:p:858-873
    DOI: 10.1016/j.amc.2019.05.053
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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.
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    6. Jau-Chuan Ke & Chuen-Horng Lin, 2005. "A Markov Repairable System Involving An Imperfect Service Station With Multiple Vacations," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 22(04), pages 555-582.
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    Cited by:

    1. Sanga, Sudeep Singh & Charan, Gannamaneni Sai, 2023. "Fuzzy modeling and cost optimization for machine repair problem with retrial under admission control F-policy and feedback," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 211(C), pages 214-240.
    2. 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.
    3. Gheisariha, Elmira & Tavana, Madjid & Jolai, Fariborz & Rabiee, Meysam, 2021. "A simulation–optimization model for solving flexible flow shop scheduling problems with rework and transportation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 180(C), pages 152-178.
    4. Mohammad Nasir & Ali Sadollah & Przemyslaw Grzegorzewski & Jin Hee Yoon & Zong Woo Geem, 2021. "Harmony Search Algorithm and Fuzzy Logic Theory: An Extensive Review from Theory to Applications," Mathematics, MDPI, vol. 9(21), pages 1-46, October.
    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. Rani, Shobha & Jain, Madhu & Meena, Rakesh Kumar, 2023. "Queueing modeling and optimization of a fault-tolerant system with reboot, recovery, and vacationing server operating under admission control policy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 209(C), pages 408-425.
    7. Cui, Ligang & Deng, Jie & Liu, Rui & Xu, Dongyang & Zhang, Yajun & Xu, Maozeng, 2020. "A stochastic multi-item replenishment and delivery problem with lead-time reduction initiatives and the solving methodologies," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    8. Shengli Lv, 2021. "Multi-Machine Repairable System with One Unreliable Server and Variable Repair Rate," Mathematics, MDPI, vol. 9(11), pages 1-16, June.
    9. Mridula Jain & Anamika Jain, 2022. "Genetic algorithm in retrial queueing system with server breakdown and caller intolerance with voluntary service," 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. 13(2), pages 582-598, April.
    10. 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.

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