Approximations of time-dependent unreliable flow lines with finite buffers

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• 作者：S. Göttlich ; S. Kühn ; J. A. Schwarz…
• 刊名：Mathematical Methods of Operations Research (ZOR)
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：83
• 期：3
• 页码：295-323
• 全文大小：1,271 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Calculus of Variations and Optimal Control
  Operation Research and Decision Theory
  Business
  
• 出版者：Physica Verlag, An Imprint of Springer-Verlag GmbH
• ISSN：1432-5217
• 卷排序：83

文摘

Flow lines process discrete workpieces on consecutive machines, which are coupled by buffers. Their operating environment is often stochastic and time-dependent. For the flow line under consideration, the stochasticity is generated by random breakdowns and successive stochastic repair times, whereas the processing times are deterministic. However, the release rate of workpieces to the line is time-dependent, due to changes in demand. The buffers between the machines may be finite or infinite. We introduce two new sampling approaches for the performance evaluation of such flow lines: one method utilizes an approximation based on a mixed-integer program in discrete time with discrete material, while the other approximation is based on partial and ordinary differential equations in continuous time and with a continuous flow of material. In addition, we sketch a proof that these two approximations are equivalent under some linearity assumptions. A computational study demonstrates the accuracy of both approximations relative to a discrete-event simulation in continuous time. Furthermore, we reveal some effects occurring in unreliable flow lines with time-dependent processing rates.KeywordsUnreliable flow lineSamplingMixed-integer programConservation lawsPiecewise deterministic process