A Novel Approach to Cell Formation

We present an approach to the cell formation problem, known from group technology, which is inspired by formal concept analysis. The cell formation problem consists in allocating parts (objects) to machines (attributes), based on the machine-part matrix. This can be viewed as forming groups consisting of a set of parts and a set of machines. Such groups resemble formal concepts in the input data. Due to the specific nature of the performance assessment in the cell formation problem, good groups can be thought of as rectangles which, unlike those corresponding to formal concepts, contain a few blanks, i.e. which are not full of crosses in terms of formal concept analysis. Moreover, such groups need to be disjoint both in terms of objects and attributes. In this paper, we present an algorithm for the cell formation problem, experimental results, and a comparison to some methods proposed in the literature.

[1]  Nallan C. Suresh,et al.  Achieving factory automation through Group Technology principles , 1985 .

[2]  Bernhard Ganter,et al.  Formal Concept Analysis, 6th International Conference, ICFCA 2008, Montreal, Canada, February 25-28, 2008, Proceedings , 2008, International Conference on Formal Concept Analysis.

[3]  Karl Pearson F.R.S..  LIII. On lines and planes of closest fit to systems of points in space , 1901 .

[4]  Claudio Carpineto,et al.  Concept data analysis - theory and applications , 2004 .

[5]  Asoo J. Vakharia,et al.  Methods of Cell Formation in Group Technology: A Framework for Evaluation , 1986 .

[6]  B. Sarker,et al.  A similarity coefficient measure and machine-parts grouping in cellular manufacturing systems , 2000 .

[7]  M SelimHassan,et al.  Cell formation in group technology , 1998 .

[8]  D. A. Milner,et al.  Direct clustering algorithm for group formation in cellular manufacture , 1982 .

[9]  Bernhard Ganter,et al.  Formal Concept Analysis: Mathematical Foundations , 1998 .

[10]  Asoo J. Vakharia,et al.  Cell formation in group technology: review, evaluation and directions for future research , 1998 .

[11]  Nancy Lea Hyer,et al.  Cellular manufacturing in the U.S. industry: a survey of users , 1989 .

[12]  Sebastián Lozano,et al.  Machine cell formation in generalized group technology , 2001 .

[13]  T. Narendran,et al.  An assignment model for the part-families problem in group technology , 1990 .

[14]  Asoo J. Vakharia,et al.  A methodology for designing flexible cellular manufacturing systems , 1997 .

[15]  V. Madhusudanan Pillai,et al.  A robust cellular manufacturing system design for dynamic part population using a genetic algorithm , 2008 .

[16]  Yong Yin,et al.  A dissimilarity measure for solving the cell formation problem in cellular manufacturing , 2001 .

[17]  Sunderesh S. Heragu,et al.  Group Technology and Cellular Manufacturing , 1994, IEEE Trans. Syst. Man Cybern. Syst..

[18]  Vilém Vychodil,et al.  Dense rectangles in object-attribute data , 2006, 2006 IEEE International Conference on Granular Computing.

[19]  J. Miltenburg,et al.  A comparative evaluation of nine well-known algorithms for solving the cell formation problem in group technology , 1991 .

[20]  Mingyuan Chen,et al.  A mathematical approach for the formation of manufacturing cells , 2005, Comput. Ind. Eng..