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Mathematical Problems in Engineering
Volume 3 (1996), Issue 2, Pages 95-171
http://dx.doi.org/10.1155/S1024123X97000501

Improvability theory for assembly systems: Two component—one assembly machine case

1Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor 48109-2122, MI, USA
2On Sabbatical leave from the Department of Electrical Engineering, Korea Advanced Institute of Science and Technology, Taejon, Korea
3Department of Aerospace Engineering, University of Michigan, Ann Arbor 48109-2140, MI, USA

Received 18 April 1996

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.

Abstract

Improvability theory for a simple assembly system consisting of two components and one assembly machine is developed. Both constrained and unconstrained formulations are addressed. In the constrained case, it is shown that the assembly is unimprovable with respect to workforce if each component machine is blocked as frequently as the assembly machine is starved for parts produced by this particular assembly machine. The system is unimprovable with respect to work-in-process if, roughly speaking, all buffers have equal average steady state occupancy. In the unconstrained improvability case, it is shown that the bottleneck machine can be identified by analyzing the probabilities of the so-called manufacturing blockages and starvations. A generalization to n component—one assembly machine system is also included.