An exact method for solving the manufacturing cell formation problem

The cell formation problem is extensively studied in the literature, but very few authors have proposed exact methods. In this paper a linear binary programming formulation is introduced to generate a solution for the cell formation problem. To verify the behaviour of the proposed model, a set of 35 benchmark problems is solved using the branch and cut method implemented in the IBM ILOG CPLEX 10.11 Optimiser. Moreover, these results allow us to validate the quality of the solution generated with heuristic methods proposed in the literature. This experimentation indicates that, for the smaller problems, the best-known solutions are the same as those generated with CPLEX 10.11 Optimiser. These results indicate a fair confidence in the optimality of the best-known solutions generated by the heuristic methods. Furthermore, our approach is the first exact method providing results of this quality.

[1]  Shih-Wei Lin,et al.  Part-machine cell formation in group technology using a simulated annealing-based meta-heuristic , 2010 .

[2]  Y. Aneja,et al.  Selection of parts and machines for cellularization: A mathematical programming approach , 1992 .

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

[4]  Ali M. S. Zalzala,et al.  Recent developments in evolutionary computation for manufacturing optimization: problems, solutions, and comparisons , 2000, IEEE Trans. Evol. Comput..

[5]  Anthony Vannelli,et al.  Strategic subcontracting for efficient disaggregated manufacturing , 1986 .

[6]  G. Srinivasan.  A clustering algorithm for machine cell formation in group technology using minimum spanning trees , 1994 .

[7]  Vinod Kumar,et al.  Entropic measures of manufacturing flexibility , 1987 .

[8]  Larry R. Taube,et al.  The facets of group technology and their impacts on implementation--A state-of-the-art survey , 1985 .

[9]  Hamid Seifoddini,et al.  A note on the similarity coefficient method and the problem of improper machine assignment in group technology applications , 1989 .

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

[11]  Kam-Fai Wong,et al.  A TSP-based heuristic for forming machine groups and part families , 1998 .

[12]  Paul J. Schweitzer,et al.  Problem Decomposition and Data Reorganization by a Clustering Technique , 1972, Oper. Res..

[13]  A. Kusiak,et al.  Efficient solving of the group technology problem , 1987 .

[14]  A. Kusiak,et al.  Similarity coefficient algorithms for solving the group technology problem , 1992 .

[15]  Tabitha L. James,et al.  A hybrid grouping genetic algorithm for the cell formation problem , 2007, Comput. Oper. Res..

[16]  Larry R. Taube,et al.  Weighted similarity measure heuristics for the group technology machine clustering problem , 1985 .

[17]  Allan S. Carrie,et al.  Numerical taxonomy applied to group technology and plant layout , 1973 .

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

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

[20]  Andrew Kusiak,et al.  Grouping of parts and components in flexible manufacturing systems , 1986 .

[21]  M. Chandrasekharan,et al.  GROUPABIL1TY: an analysis of the properties of binary data matrices for group technology , 1989 .

[22]  F. Boctor.  A Jinear formulation of the machine-part cell formation problem , 1991 .

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

[24]  Warren J. Boe,et al.  A close neighbour algorithm for designing cellular manufacturing systems , 1991 .

[25]  Larry E. Stanfel,et al.  Machine clustering for economic production , 1985 .

[26]  Ming Liang,et al.  Comparative study of simulated annealing, genetic algorithms and tabu search for solving binary and comprehensive machine-grouping problems , 2002 .

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

[28]  M. Chandrasekharan,et al.  MODROC: an extension of rank order clustering for group technology , 1986 .

[29]  Manojit Chattopadhyay,et al.  Genetic Rule Based Techniques in Cellular Manufacturing (1992-2010): A Systematic Survey , 2010 .

[30]  C. Hicks,et al.  An Enhanced Grouping Genetic Algorithm for solving the cell formation problem , 2009 .

[31]  Maghsud Solimanpur,et al.  Genetic algorithm approach for solving a cell formation problem in cellular manufacturing , 2009, Expert Syst. Appl..

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

[33]  Christos Dimopoulos,et al.  A hierarchical clustering methodology based on genetic programming for the solution of simple cell-formation problems , 2001 .

[34]  M. Chandrasekharan,et al.  ZODIAC—an algorithm for concurrent formation of part-families and machine-cells , 1987 .

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

[36]  Ali Husseinzadeh Kashan,et al.  A differential evolution algorithm for the manufacturing cell formation problem using group based operators , 2010, Expert Syst. Appl..

[37]  Mauricio G. C. Resende,et al.  An evolutionary algorithm for manufacturing cell formation , 2004, Comput. Ind. Eng..

[38]  B. Sarker,et al.  A comparison of existing grouping efficiency measures and a new weighted grouping efficiency measure , 2001 .

[39]  graphics , 1991 .

[40]  Chung-Cheng Lu,et al.  Cell formation using a simulated annealing algorithm with variable neighbourhood , 2011 .

[41]  Divakar Rajamani,et al.  A mathematical model for cell formation considering investment and operational costs , 1993 .

[42]  Iraj Mahdavi,et al.  Designing a new mathematical model for cellular manufacturing system based on cell utilization , 2007, Appl. Math. Comput..

[43]  P. Waghodekar,et al.  Machine-component cell formation in group technology: MACE , 1984 .

[44]  Yash P. Aneja,et al.  An ant colony optimization metaheuristic for machine-part cell formation problems , 2010, Comput. Oper. Res..

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

[46]  John M. Wilson,et al.  The evolution of cell formation problem methodologies based on recent studies (1997-2008): Review and directions for future research , 2010, Eur. J. Oper. Res..