Math Meth Oper Res DOI 10.1007/s00186-015-0529-6 Approximations of time-dependent unreliable flow lines with finite buffers S. Göttlich 1 · S. Kühn 1 · J. A. Schwarz 2 · R. Stolletz 2 Received: 19 February 2015 / Accepted: 22 December 2015 © Springer-Verlag Berlin Heidelberg 2016 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. B S. Göttlich goettlich@uni-mannheim.de; goettlich@math.uni-mannheim.de S. Kühn sekuehn@math.uni-mannheim.de J. A. Schwarz schwarz@bwl.uni-mannheim.de R. Stolletz stolletz@bwl.uni-mannheim.de 1 School of Business Informatics and Mathematics, University of Mannheim, 68131 Mannheim, Germany 2 Business School, University of Mannheim, 68131 Mannheim, Germany 123