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A New Improved Aggregation Algorithm for Performance Metric Calculation in Serial Production Lines with Exponential Machines



Peter O. Denno, Yishu Bai, Tu Jiachen, Yang Mengzhao, Liang Zhang


Performance metric calculation is one of the most important problems in production systems research. In this paper, we consider serial production lines with finite buffers and machines following the exponential reliability model. Analytical formulas are first given for performance analysis of two-machine lines. Based on these formulas, a throughput-equivalent aggregation procedure is derived to represent a two- machine exponential line by a single exponential machine. Following this approach, we propose a new aggregation-based iterative algorithm to calculate the performance metrics of a multi-machine serial line by representing it using a group of virtual two-machine lines. Extensive numerical experiments are used to justify the convergence of the algorithm and to evaluate the accuracy of the calculated performance metrics. The results show that the proposed algorithm significantly improve the performance metric approximation accuracy, compared to a commonly used aggregation-based method in the literature, without incurring additional computational burden. The improvement is even more prominent for systems with relatively small buffers. We believe that this work makes an important contribution to the field of Production Systems Engineering and has the potential to generate great impact as the new algorithm replaces the existing one in future research and applications by scholars and practitioners.
International Journal of Production Research


serial production line, performance metric calculation, exponential machine, aggregation


Denno, P. , Bai, Y. , Jiachen, T. , Mengzhao, Y. and Zhang, L. (2022), A New Improved Aggregation Algorithm for Performance Metric Calculation in Serial Production Lines with Exponential Machines, International Journal of Production Research (Accessed June 23, 2024)


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Created October 4, 2022