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Mathematical Problems in Engineering
Volume 2, Issue 3, Pages 233-276

Bottlenecks in serial production lines: A system-theoretic approach

Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor 48109-2122, MI, USA

Received 9 November 1995

Copyright © 1996 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this work, a new definition of production systems bottlenecks is formulated and analyzed. Specifically, a machine is defined as the bottleneck if the sensitivity of the system's performance index to this machine's production rate in isolation is the largest. Although appealing from the systems point of view, this definition suffers a deficiency due to the fact that the sensitivities involved cannot be either measured on-line or efficiently calculated off-line. To avoid this, the paper develops a method based on indirect but real-time data. From this point of view, the main result of the work is as follows: The bottleneck machine in a serial production line can be identified by analyzing relationships between the so-called manufacturing blockage and manufacturing starvation of each machine. This leads to a simple rule for bottleneck identification. The rule requires neither the calculation of the production rate sensitivities nor the production rate itself. When the probabilities of manufacturing blockages and starvations are not available from on-line measurements, the paper presents their analytical estimates which, under certain conditions, can be used for bottleneck identification. Finally, a case study at an automotive component plant is described.