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Mathematical Problems in Engineering
Volume 2006, Article ID 27328, 12 pages

Conservation of filtering in manufacturing systems with unreliable machines and finished goods buffers

1Manufacturing Systems Research Laboratory, GM Research & Development Center, Warren 48090-9055, MI, USA
2Decision Applications Division, Los Alamos National Laboratory, Los Alamos 87545, NM, USA
3Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor 48109-2122, MI, USA

Received 22 April 2005; Accepted 22 April 2005

Copyright © 2006 Jingshan Li et al. 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.


This paper addresses the issue of reliable satisfaction of customer demand by unreliable production systems. In the framework of a simple production-storage-customer model, we show that this can be accomplished by using an appropriate level of filtering of production randomness. The filtering is ensured by finished goods buffers (filtering in space) and shipping periods (filtering in time). The following question is considered: how are filtering in space and filtering in time interrelated? As an answer, we show that there exists a conservation law: in lean manufacturing systems, the amount of filtering in space multiplied by the amount of filteringin time (both measured in appropriate dimensionless units) ispractically constant. Along with providing an insight into the nature of manufacturing systems, this law offers a tool for selecting the smallest, that is, lean, finished goods buffering, which is necessary and sufficient to ensure the desired level ofcustomer demand satisfaction.