On NP-completeness of the cell formation problem

In the current paper we provide a proof of NP-completeness for the CFP problem with the fractional grouping efficacy objective. For this purpose we first consider the CFP with the linear objective minimizing the total number of exceptions and voids. Following the ideas of Pinheiro et al. (2016) we show that it is equivalent to the Bicluster Graph Editing Problem (BGEP), which is known to be NP-complete (Amit, 2004). Then we suggest a reduction of the CFP problem with the linear objective function to the CFP with the grouping efficacy objective.

[1]  Jacques A. Ferland,et al.  An exact method for solving the manufacturing cell formation problem , 2012 .

[2]  Ivan C. Martins,et al.  On Solving Manufacturing Cell Formation via Bicluster Editing , 2013, Eur. J. Oper. Res..

[3]  Panos M. Pardalos,et al.  Exact model for the cell formation problem , 2014, Optim. Lett..

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

[5]  Felix T.S. Chan,et al.  Cell formation problem with consideration of both intracellular and intercellular movements , 2008 .

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

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

[8]  Mohammad Mahdi Paydar,et al.  A hybrid genetic-variable neighborhood search algorithm for the cell formation problem based on grouping efficacy , 2013, Comput. Oper. Res..

[9]  Maghsud Solimanpur,et al.  Solving cell formation problem in cellular manufacturing using ant-colony-based optimization , 2010 .

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

[11]  Kai-Ling Mak,et al.  An Adaptive Genetic Algorithm for Manufacturing Cell Formation , 2000 .

[12]  J. Arkat,et al.  A new branch and bound algorithm for cell formation problem , 2012 .

[13]  Beverly Sackler,et al.  The Bicluster Graph Editing Problem , 2004 .

[14]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[15]  Dana S. Nau,et al.  Manufacturing cell formation by state-space search , 1996, Ann. Oper. Res..

[16]  Warren J. Boe,et al.  DESIGNING CELLULAR MANUFACTURING SYSTEMS: BRANCH-AND-BOUND AND A∗ APPROACHES , 1993 .

[17]  Tai-Hsi Wu,et al.  An efficient tabu search algorithm to the cell formation problem with alternative routings and machine reliability considerations , 2011, Comput. Ind. Eng..

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

[19]  Panos M. Pardalos,et al.  Models, algorithms, and technologies for network analysis , 2013 .

[20]  Panos M. Pardalos,et al.  Heuristic Algorithm for the Cell Formation Problem , 2013 .

[21]  Irina Utkina,et al.  A Branch and Bound Algorithm for a Fractional 0-1 Programming Problem , 2016, DOOR.

[22]  S. Sofianopoulou,et al.  An optimal tree search method for the manufacturing systems cell formation problem , 1998, Eur. J. Oper. Res..

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