Approximations of time-dependent unreliable flow lines with finite buffers

Göttlich, Simone ; Kühn, Sebastian ; Schwarz, Justus Arne ; Stolletz, Raik

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Document Type: Article
Year of publication: 2016
The title of a journal, publication series: Mathematical Methods of Operations Research
Volume: 83
Issue number: 3
Page range: 295-323
Place of publication: Berlin ; Heidelberg
Publishing house: Springer
ISSN: 1432-2994 , 0340-9422
Publication language: English
Institution: School of Business Informatics and Mathematics > Wissenschaftliches Rechnen (Göttlich 2011-)
Business School > ABWL u. Produktion (Stolletz)
Subject: 330 Economics
Keywords (English): Unreliable flow line ; Sampling ; Mixed-integer program ; Conservation laws ; Piecewise deterministic process
Abstract: 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.

Dieser Eintrag ist Teil der Universitätsbibliographie.

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