# A Metaheuristic algorithm for the manufacturing cell formation problem based on grouping efficacy

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## Abstract

The cell formation problem determines decomposition of the manufacturing cells of a production system. Machines are assigned to the cells to process one or more part families so that each cell is operated independently and the inter-cellular movements are minimized. This paper proposes a new algorithm for grouping problems (bin packing, graph coloring, scheduling, etc.) which is a grouping version of an almost new algorithm (league championship algorithm (LCA)), and we used it to solve benchmarked instances of cell formation problem posing as a grouping problem. To evaluate the effectiveness of our approach, we borrow a set of 35 most widely used benchmark problem instances from literature and compare the performance of grouping LCA (GLCA) and several well-known algorithms published. The proposed algorithm can reach the best solution for 29 of the 35 benchmark problems and differs with the best-known solution of three benchmark problems only with 0.7 % average gap. We also used a new method to find the number of initial cells. The results show that GLCA may hopefully be a new approach for such kinds of difficult-to-solve problems. Moreover, a real-world industrial case is provided to show how the proposed algorithm works. Considering the performance of the GLCA algorithm on all test problems, the proposed algorithm should thus be useful to both practitioners and researchers.

## Keywords

Cell formation problem Grouping genetic algorithm League championship algorithm## Preview

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## References

- 1.Anvari M, Mehrabad M, Barzinpour F (2010) Machine-part cell formation using a hybrid particle swarm optimization. Int J Adv Manuf Technol 2010:745–754CrossRefGoogle Scholar
- 2.Askin RG, Subramanian SP (1987) A cost-based heuristic for group technology configuration. Int J Prod Res 25:101–113CrossRefGoogle Scholar
- 3.Ateme-Nguem B, Dao T (2007) Optimization of cellular manufacturing systems design using the hybrid approach based on the ant colony and tabu search techniques. In Proceedings of the IEEE IEEM, pages 668–673Google Scholar
- 4.Ateme-Nguema B, Dao T (2009) Quantized Hopfield networks and tabu search for manufacturing cell formation problems. Int J Prod Res 121:88–98CrossRefGoogle Scholar
- 5.Batsyn M, Bychkov I, Goldengorin B, Pardalos P, Sukhov P (2013) Pattern-based heuristic for the cell formation problem in group technology. B. Goldengorin et al. (eds.), Models, algorithms, and technologies for network analysis, Springer Proceedings in Mathematics & Statistics, 32, 11-50Google Scholar
- 6.Boctor FF (1991) A linear formulation of the machine-part cell formation problem. Int J Prod Res 29:343–356CrossRefGoogle Scholar
- 7.Boe WJ, Cheng CH (1991) A close neighbor algorithm for designing cellular manufacturing systems. Int J Prod Res 29:2097–2116CrossRefMATHGoogle Scholar
- 8.Boulif M, Atif K (2006) A new branch-&-bound-enhanced genetic algorithm for the manufacturing cell formation problem. Comput Oper Res 33:2219–2245CrossRefMATHGoogle Scholar
- 9.Boutsinas B (2013) Machine-part cell formation using biclustering. Eur J Oper Res 230:563–572MathSciNetCrossRefGoogle Scholar
- 10.Brown E, James T (2007) A hybrid grouping genetic algorithm for the cell formation problem. Comput Oper Res 34:2059–2079CrossRefMATHGoogle Scholar
- 11.Brown E, Sumichrast R (2001) CF-GGA: a grouping genetic algorithm for the cell formation problem. Int J Prod Res 36:3651–3669CrossRefGoogle Scholar
- 12.Carrie AS (1973) Numerical taxonomy applied to group technology and plant layout. Int J Prod Res 399-416Google Scholar
- 13.Chan HM, Milner DA (1982) Direct clustering algorithm for group formation in cellular manufacturing. Journal of Manufacturing Systems 1: 65–74Google Scholar
- 14.Chandrasekharan MP, Rajagopalan R (1986) MODROC: an extension of rank order clustering for group technology. Int J Prod Res 24:1221–1233CrossRefGoogle Scholar
- 15.Chandrasekharan MP, Rajagopalan R (1986) An ideal seed non-hierarchical clustering algorithm for cellular manufacturing. Int J Prod Res 24:451–463CrossRefMATHGoogle Scholar
- 16.Chandrasekharan MP, Rajagopalan R (1989) Groupability: an analysis of the properties of binary data matrices for group technology. Int J Prod Res 27:1035–1052CrossRefGoogle Scholar
- 17.Cheng C, Gupa Y, Lee WA (1998) TSP-based heuristic for forming machine groups and part families. Int J Prod Res 36:1325–1337CrossRefMATHGoogle Scholar
- 18.DeLit P, Falkenauer E, Delchambre A (2000) Grouping genetic algorithms: an efficient method to solve the cell formation problem. Math Comput Simul 51:257–271CrossRefGoogle Scholar
- 19.Elbenani B, Ferland J, Bellemare J (2012) Genetic algorithm and large neighborhood search to solve the cell formation problem. Expert Syst ApplGoogle Scholar
- 20.Falkenauer E (1998) Genetic algorithm for grouping problems. Wiley, New YorkGoogle Scholar
- 21.Ghosh T, Sengupta S, Chattopadhyay M, Dan KP (2011) Meta-heuristics in cellular manufacturing: a state-of-art review. Int J Ind EngComput 2:87–122Google Scholar
- 22.Goldengorin B, Krushinsky D, Slomp J (2012) Flexible PMP approach for large size cell formation. Oper Res 60:1157–1166MathSciNetCrossRefMATHGoogle Scholar
- 23.Goncalves J, Resende M (2004) An evolutionary algorithm for manufacturing cell formation. Comput Ind Eng 47:247–273CrossRefGoogle Scholar
- 24.Heragu SS (1997) Facility design. PWS Publishing Company, BostonGoogle Scholar
- 25.Husseinzadeh Kashan A (2009) League championship algorithm: a new algorithm for numerical function optimization. International Conference of Soft Computing and Pattern RecognitionGoogle Scholar
- 26.Husseinzadeh Kashan A, Karimi B, Jolai F (2006) Effective hybrid genetic algorithm for minimizing makespan on a single-batch-processing machine with non-identical job sizes. Int J Prod Res 44:2337–2360CrossRefGoogle Scholar
- 27.Husseinzadeh Kashan A, Karimi B, Noktehdan A (2014) A novel discrete particle swarm optimization algorithm for the manufacturing cell formation problem. Int J Adv Manuf TechnolGoogle Scholar
- 28.King JR (1980) Machine-component grouping in production flow analysis: an approach using a rank order clustering algorithm. Int J Prod Res 213-232Google Scholar
- 29.King JR, Nakornchai V (1982) Machine-component group formation in group technology: review and extension. Int J Prod Res 20:117–131CrossRefGoogle Scholar
- 30.Krushinsky D, Goldengorin B (2012) An exact model for cell formation in group technology. Comput Manag Sci 9:323–338MathSciNetCrossRefMATHGoogle Scholar
- 31.Kumar C, Chandrasekharan MP (1990) Grouping efficacy: a quantitative criterion for goodness of block diagonal forms of binary matrix in group technology. Int J Prod Res 28:233–243CrossRefGoogle Scholar
- 32.Kumar KR, Kusiak A, Vannelli A (1986) Grouping of parts and components in flexible manufacturing systems. Eur J Oper Res 24:387–397CrossRefGoogle Scholar
- 33.Kusiak A, Cho M (1992) Similarity coefficient algorithm for solving the group technology problem. Int J Prod Res 30:2633–263346CrossRefGoogle Scholar
- 34.Kusiak A, Chow WS (1987) Efficient solving of the group technology problem. J Manuf Syst 6:117–124CrossRefGoogle Scholar
- 35.Lei D, Wu Z (2005) Tabu search approach based on a similarity coefficient for cell formation in generalized group technology. Int J Prod Res 19:4035–4047CrossRefGoogle Scholar
- 36.Lei D, Wu Z (2006) Tabu search for multiple-criteria manufacturing cell design. Int J Adv Manuf Technol 28:950–956CrossRefGoogle Scholar
- 37.McCormick WT, Schweitzer PJ, White TW (1972) Problem decomposition and data reorganization by a clustering technique. Oper Res 20:993–1009CrossRefMATHGoogle Scholar
- 38.Mosier CT, Taube L (1985) The facets of group technology and their impact on implementation. OMEGAGoogle Scholar
- 39.Mosier CT, Taube L (1985) Weighted similarity measure heuristics for the group technology machine clustering problem. OMEGAGoogle Scholar
- 40.Noktehdan A, Karimi B, Husseinzadehkashan A (2010) A differential evolution algorithm for the manufacturing cell formation problem using group based operators. Expert Syst Appl 37:4822–4829CrossRefGoogle Scholar
- 41.Noktehdan A, Seyedhosseini SM, Saidi-Mehrabad M (2015) A Metaheuristic algorithm for the manufacturing cell formation problem based on grouping efficacy. Int J Adv Manuf TechnolGoogle Scholar
- 42.Pailla A, Trindade A, Parada V, Ochi L (2010) A numerical comparison between simulated annealing and evolutionary approaches to the cell formation problem. Expert Syst Appl 37:5476–5483CrossRefGoogle Scholar
- 43.Prabhaharan G, Muruganandam A, Asokanm P, Girish BS (2005) Machine cell formation for cellular manufacturing systems using an ant colony system approach. Int J Adv Manuf Technol 25:1013–1019CrossRefGoogle Scholar
- 44.Rao PK (2014) A multi stage heuristic for manufacturing cell formation. Int J Res EngTechnol 1163:2308–2321Google Scholar
- 45.Roy N, Komma VR (2014) Cellular manufacturing through composite part formation: a genetic algorithm approach. International Conference on Industrial Engineering and Operations Management, Bali, Indonesia, January 7 – 9Google Scholar
- 46.Sarker B (2001) Measures of grouping efficacy in cellular manufacturing systems. Eur J Oper Res 130:588–611CrossRefMATHGoogle Scholar
- 47.Sayadi MK, Hafezalkotob A, Jalali naini SG (2013) Firefly-inspired algorithm for discrete optimization problems: an application to manufacturing cell formation. J Manuf Syst 32:78–84CrossRefGoogle Scholar
- 48.Seifoddini H (1989) A note on the similarity coefficient method and the problem of improper machine assignment in group technology applications. Int J Prod Res 27: 1161–1165Google Scholar
- 49.Seifoddini H, Wolf PM (1986) Application of the similarity coefficient method in group technology. IIIE Transaction 18: 271--277Google Scholar
- 50.Selim HM, Askin RG, Vakharia AJ (1998) Cell formation in group technology: evaluation and directions for future research. Comput Ind Eng 34:3–20CrossRefGoogle Scholar
- 51.Solimanpur M, Saeedi S, Mahdavi I (2010) Solving cell formation problem in cellular manufacturing using ant-colony-based optimization. Int J Adv Manuf Technol 50:1135–1144CrossRefGoogle Scholar
- 52.Stanfel LE (1985) Machine clustering for economic production. Eng Costs Prod Econ 9:73–81CrossRefGoogle Scholar
- 53.Stawowy A (2006) Evolutionary strategy for manufacturing cell design. Omega, Int J Manag Sci 34:1–18CrossRefGoogle Scholar
- 54.Sun D, Lin L, Batta R (1995) Cell formation using tabu search. Comput Ind Eng 28:485–494CrossRefGoogle Scholar
- 55.Vin E, DeLit P, Delchamber A (2005) A multiple-objective grouping genetic algorithm for the cell formation problem with alternative routings. J Intell Manuf 16:189–205CrossRefGoogle Scholar
- 56.Waghodekar PH, Sahu S (1984) Machine-component cell formation in group technology MACE. Int J Prod Res 22:937–948CrossRefGoogle Scholar
- 57.Wemmerlov U, Hyer NL (1989) Cellular manufacturing in the US industry: a survey of users. Int J Prod Res 27:1511–1530CrossRefGoogle Scholar
- 58.Wu T, Chang C, Chung S (2008) A simulated annealing algorithm for manufacturing cell formation problems. Expert Syst ApplGoogle Scholar
- 59.Wu T, Chang C, Yeh J (2009) A hybrid heuristic algorithm adopting both Boltzmann function and mutation operator for manufacturing cell formation problems. Int J Prod Econ 120:669–688CrossRefGoogle Scholar
- 60.Wu T, Chung S, Chang C (2010) A water flow-like algorithm for manufacturing cell formation problems. Eur J Oper Res 205:346–360CrossRefMATHGoogle Scholar