Performance analysis of production lines with continuous material flows and finite buffers

This paper deals with the approximative analysis of production lines with continuous material flow consisting of a number of machines or servers in series and finite buffers in between. Each server suffers from operational dependent breakdowns, characterized by exponentially distributed up- and down-times. We construct an iterative method to efficiently and accurately estimate performance characteristics such as throughput and mean total buffer content. The method is based on decomposition of the production line into single-buffer subsystems. Novel features of the method are (i) modeling of the aggregate servers in each subsystem, (ii) equations to iteratively determine the processing behavior of these servers, and (iii) use of modern matrix-analytic techniques to analyze each subsystem. The proposed method performs very well on a large test set, including long and imbalanced production lines. For production lines with imbalance in mean down-times, we show that a more refined modeling of the servers in each subsystem performs significantly better. Lastly, we apply the iterative method to predict the throughput of a bottle line at brewery Heineken Den Bosch yielding errors of less than two percent.