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Analysis of a general Markovian two-stage continuous-flow production system with a finite buffer

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  • Tan, BarIs
  • Gershwin, Stanley B.

Abstract

Fluid flow models are used in the performance evaluation of production, computer, and telecommunication systems. In order to develop a methodology to analyze general Markovian continuous material flow production systems with two processing stages with an intermediate finite buffer, a general single-buffer fluid flow system is modelled as a continuous time, continuous-discrete state space stochastic process and the steady-state distribution is determined. Various performance measures such as the production rate and the expected buffer level are determined from the steady-state distributions. The flexibility of this methodology allows analysis of a wide range of models by specifying only the transition rates and the flow rates associated with the discrete states of each stage. Therefore, the method is proposed as a tool for performance evaluation of general Markovian continuous-flow systems with a finite buffer. The solution methodology is illustrated by analyzing a production system where each machine has multiple up and down states associated with their quality characteristics.

Suggested Citation

  • Tan, BarIs & Gershwin, Stanley B., 2009. "Analysis of a general Markovian two-stage continuous-flow production system with a finite buffer," International Journal of Production Economics, Elsevier, vol. 120(2), pages 327-339, August.
    • Handle: RePEc:eee:proeco:v:120:y:2009:i:2:p:327-339
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    References listed on IDEAS

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    1. Tan, Baris, 1998. "Effects of variability on the due-time performance of a continuous materials flow production system in series," International Journal of Production Economics, Elsevier, vol. 54(1), pages 87-100, January.
    2. Stefan Helber & Hanifa Jusić, 2004. "A New Decomposition Approach for Non-Cyclic Continuous Material Flow Lines with a Merging Flow of Material," Annals of Operations Research, Springer, vol. 125(1), pages 117-139, January.
    3. Yeralan, Sencer & Franck, Wallace E. & Quasem, Mohammad A., 1986. "A continuous materials flow production line model with station breakdown," European Journal of Operational Research, Elsevier, vol. 27(3), pages 289-300, December.
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    Cited by:

    1. Elisa Gebennini & Andrea Grassi & Cesare Fantuzzi, 2015. "The two-machine one-buffer continuous time model with restart policy," Annals of Operations Research, Springer, vol. 231(1), pages 33-64, August.
    2. Wei, Shuaichong & Nourelfath, Mustapha & Nahas, Nabil, 2023. "Analysis of a production line subject to degradation and preventive maintenance," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    3. Fitouhi, Mohamed-Chahir & Nourelfath, Mustapha & Gershwin, Stanley B., 2017. "Performance evaluation of a two-machine line with a finite buffer and condition-based maintenance," Reliability Engineering and System Safety, Elsevier, vol. 166(C), pages 61-72.
    4. Liu, Jialu & Yang, Sheng & Wu, Aiguo & Hu, S. Jack, 2012. "Multi-state throughput analysis of a two-stage manufacturing system with parallel unreliable machines and a finite buffer," European Journal of Operational Research, Elsevier, vol. 219(2), pages 296-304.
    5. Barış Tan, 2019. "Production Control with Price, Cost, and Demand Uncertainty," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(4), pages 1057-1085, December.
    6. Jean-Sébastien Tancrez, 2020. "A decomposition method for assembly/disassembly systems with blocking and general distributions," Flexible Services and Manufacturing Journal, Springer, vol. 32(2), pages 272-296, June.
    7. Shi, Chuan & Gershwin, Stanley B., 2016. "Part sojourn time distribution in a two-machine line," European Journal of Operational Research, Elsevier, vol. 248(1), pages 146-158.
    8. Zhang, Ning & Qi, Faqun & Zhang, Chengjie & Zhou, Hongming, 2022. "Joint optimization of condition-based maintenance policy and buffer capacity for a two-unit series system," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    9. Kucuksayacigil, Fikri & Roni, Mohammad & Eksioglu, Sandra D. & Bhuiyan, Tanveer H. & Chen, Qiushi, 2022. "Optimal control to handle variations in moisture content and reactor in-feed rate," Energy, Elsevier, vol. 248(C).
    10. Yaghoubi, Saeed & Noori, Siamak & Azaron, Amir & Fynes, Brian, 2015. "Resource allocation in multi-class dynamic PERT networks with finite capacity," European Journal of Operational Research, Elsevier, vol. 247(3), pages 879-894.
    11. Kolb, Oliver & Göttlich, Simone, 2015. "A continuous buffer allocation model using stochastic processes," European Journal of Operational Research, Elsevier, vol. 242(3), pages 865-874.
    12. Hatice Ucar Guner & Alper Murat & Ratna Babu Chinnam, 2024. "Performance analysis of a production system with two deteriorating machines and a finite buffer," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 32(3), pages 621-651, September.
    13. Andrea Matta & Francesca Simone, 2016. "Analysis of two-machine lines with finite buffer, operation-dependent and time-dependent failure modes," International Journal of Production Research, Taylor & Francis Journals, vol. 54(6), pages 1850-1862, March.
    14. Barış Tan & Stanley Gershwin, 2011. "Modelling and analysis of Markovian continuous flow systems with a finite buffer," Annals of Operations Research, Springer, vol. 182(1), pages 5-30, January.
    15. Ünsal Özdoğru & Tayfur Altiok, 2015. "Continuous material flow systems: analysis of marine ports handling bulk materials," Annals of Operations Research, Springer, vol. 231(1), pages 79-104, August.
    16. Marcello Colledani & Stanley Gershwin, 2013. "A decomposition method for approximate evaluation of continuous flow multi-stage lines with general Markovian machines," Annals of Operations Research, Springer, vol. 209(1), pages 5-40, October.
    17. Cruz, F.R.B. & Van Woensel, T. & Smith, J. MacGregor, 2010. "Buffer and throughput trade-offs in M/G/1/K queueing networks: A bi-criteria approach," International Journal of Production Economics, Elsevier, vol. 125(2), pages 224-234, June.
    18. Yaghoubi, Saeed & Noori, Siamak & Azaron, Amir & Tavakkoli-Moghaddam, Reza, 2011. "Resource allocation in dynamic PERT networks with finite capacity," European Journal of Operational Research, Elsevier, vol. 215(3), pages 670-678, December.

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