Approximate performance analysis of production lines with continuous material flows and finite buffers

In this paper, we analyze production lines consisting of a number of machines in series with a finite buffer between each pair of machines. The flow of products through the machines is continuous. Each machine suffers from breakdowns, because of, for example, failures, cleaning and changeover. The up- and downtimes are independent and generally distributed. We develop a novel method to efficiently and accurately estimate the throughput and the mean buffer content of the production line. This method relies on decomposition of the production line into two-stage, one-buffer subsystems aggregating the up- and downstream part of the line. It is the use of aggregation of machine speeds, starvation times and blocking times, in combination with numerically stable matrix-analytic techniques for the steady-state subsystem analysis, that renders an efficient iterative method, capable of evaluating long production lines. We demonstrate that the proposed method performs well on a large test set consisting of over 49,000 cases, including production lines of up to 16 machines. Remarkably, the performance of the method does not deteriorate in case of highly unpredictable up- and downtimes, as often seen in practice. We apply the method to a bottling line at brewery Heineken Den Bosch and an assembly line at NXP Semiconductors. Keywords: Approximation, Decomposition, Finite buffer, Fluid flow, Matrix-analytic method, Production line