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Histogram based bounds and approximations for production lines

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  • TRAZNCREZ, Jean-Sébastien
  • SEMAL, Pierre
  • CHEVALIER, Philippe

Abstract

We present a modelling method for the analysis of production lines with generally distributed processing times and finite buffers. We consider the complete modelling process, from the data collection to the performance evaluation. First, the data about the processing times is supposed to be collected in the form of histograms. Second, tractable discrete phase-type distributions are built. Third, the evolution of the production line is described by a Markov chain, using a state model. Our originality mostly comes from the way the phase-type distributions are built: the "grouping at the end" discretization aggregates the probability mass in a time step at its end. The method allows to compute refinable upper and lower bounds on the throughput. Furthermore, we propose some approximations and show how the method performs on simple examples. We argue that the way the distributions are discretized, called "probability masses fitting", can be thought as a valuable alternative in order to build tractable distributions.
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Suggested Citation

  • TRAZNCREZ, Jean-Sébastien & SEMAL, Pierre & CHEVALIER, Philippe, 2009. "Histogram based bounds and approximations for production lines," LIDAM Reprints CORE 2163, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:2163
    DOI: 10.1016/j.ejor.2008.03.032
    Note: In : European Journal of Operational Research, 197, 1133-1141, 2009
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    References listed on IDEAS

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    1. Papadopoulos, H. T. & Heavey, C., 1996. "Queueing theory in manufacturing systems analysis and design: A classification of models for production and transfer lines," European Journal of Operational Research, Elsevier, vol. 92(1), pages 1-27, July.
    2. Kerbache, Laoucine & Smith, J. MacGregor, 2000. "Multi-objective routing within large scale facilities using open finite queueing networks," European Journal of Operational Research, Elsevier, vol. 121(1), pages 105-123, February.
    3. Gourgand, Michel & Grangeon, Nathalie & Norre, Sylvie, 2005. "Markovian analysis for performance evaluation and scheduling in m machine stochastic flow-shop with buffers of any capacity," European Journal of Operational Research, Elsevier, vol. 161(1), pages 126-147, February.
    4. Yves Dallery & Yannick Frein, 1993. "On Decomposition Methods for Tandem Queueing Networks with Blocking," Operations Research, INFORMS, vol. 41(2), pages 386-399, April.
    5. C Dinçer & B Deler, 2000. "On the distribution of throughput of transfer lines," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(10), pages 1170-1178, October.
    6. Laoucine Kerbache & J. Macgregor Smith, 2000. "Multi-objective routing within large scale facilities using open finite queueing networks," Post-Print hal-00798811, HAL.
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    Cited by:

    1. Jean-Sébastien Tancrez & Philippe Chevalier & Pierre Semal, 2011. "Probability masses fitting in the analysis of manufacturing flow lines," Annals of Operations Research, Springer, vol. 182(1), pages 163-191, January.
    2. 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.

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