Polyhedral dynamics as a tool for machine-part group formation

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Abstract
It has been suggested that the efficiency and economics of a flexible manufacturing system can be improved through judicious grouping of machines and parts. This paper addresses the formulation of families of parts requiring similar manufacturing with closely related machines using the topological concepts of polyhedral dynamics (i.e. q-analysis). An introduction to the concepts of q-analysis is presented and is followed by a discussion of the application to machine-part group formation. Two examples from the literature are presented and the resulting part groupings compared. The results suggest that q-analysis not only provides part grouping capabilities equivalent to current techniques, but also provides additional qualitative information. Measures are available which provide insight into the importance of particular groupings and the strength of the interaction between the groups. The analysis also identifies machines with are potential bottlenecks, and parts whose availability may impact the manufacturing process. A measure is also available for comparing various flexible manufacturing system options in terms of process stability or controllability through a qualitative estimate of system complexity.

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