Optimal solution of cellular manufacturing system design: Benders' decomposition approach

In this paper, a mathematical model for cellular manufacturing system (CMS) design which incorporates three critical aspects - resource utilization, alternate routings, and practical constraints, is presented. The model is shown to be NP-complete. A linear, mixed-integer version of the model which not only has fewer integer variables compared to most other models in the literature, but one that also permits us to solve it optimally using Benders' decomposition approach is presented. Some results that allow us to solve the problem efficiently as well as computational results with Benders' decomposition algorithm and a modified version are presented.

[1]  Philip M. Wolfe,et al.  Application of the Similarity Coefficient Method in Group Technology , 1986 .

[2]  John McAuley,et al.  Machine grouping for efficient production , 1972 .

[3]  N. Singh,et al.  Design of cellular manufacturing systems: An invited review , 1993 .

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

[5]  M. Chandrasekharan,et al.  An ideal seed non-hierarchical clustering algorithm for cellular manufacturing , 1986 .

[6]  Sunderesh S. Heragu,et al.  Grouping and placement of machine cells , 1997 .

[7]  J. King.  Machine-component grouping in production flow analysis: an approach using a rank order clustering algorithm , 1980 .

[8]  Divakar Rajamani,et al.  Design of cellular manufacturing systems , 1996 .

[9]  Ronald G. Askin,et al.  A graph partitioning procedure for machine assignment and cell formation in group technology , 1990 .

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

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

[12]  M. Chandrasekharan,et al.  Grouping efficacy: a quantitative criterion for goodness of block diagonal forms of binary matrices in group technology , 1990 .

[13]  Harold J. Steudel,et al.  A within-cell utilization based heuristic for designing cellular manufacturing systems , 1987 .

[14]  G. K. Adil,et al.  Assignment allocation and simulated annealing algorithms for cell formation , 1997 .

[15]  John L. Burbidge,et al.  The introduction of group technology , 1975 .

[16]  K. Hitomi,et al.  GT cell formation for minimizing the intercell parts flow , 1992 .

[17]  A. M. Geoffrion,et al.  Multicommodity Distribution System Design by Benders Decomposition , 1974 .

[18]  Abraham Mehrez,et al.  Cellular manufacturing: A taxonomic review framework , 1994 .

[19]  Josef Stoer,et al.  Numerische Mathematik 1 , 1989 .

[20]  Sunderesh S. Heragu,et al.  A heuristic for designing cellular manufacturing facilities , 1994 .

[21]  G. Srinivasan,et al.  GRAFICS—a nonhierarchical clustering algorithm for group technology , 1991 .

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

[23]  Nancy Lea Hyer,et al.  Procedures for the part family/machine group identification problem in cellular manufacturing , 1986 .

[24]  J. King,et al.  Machine-component group formation in group technology: review and extension , 1982 .

[25]  Sung-Lyong Kang,et al.  A work load-oriented heuristic methodology for manufacturing cell formation allowing reallocation of operations , 1993 .

[26]  Abraham Mehrez,et al.  Formulation of the machine cell grouping problem with capacity and material movement constraints , 1994 .

[27]  Ronald G. Asktn,et al.  A cost-based heuristic for group technology configuration† , 1987 .