Document Type : Original Article

Authors

1 Mazandaran University of Science and Technology, Department of Industrial Engineering, Babol, Iran.

2 Babol Noshirvani University of Technology, Department of Industrial Engineering, Babol, Iran.

Abstract

Cell formation problem (CFP) is one of the main problems in cellular manufacturing systems. Minimizing exceptional elements and voids is one of the common objectives in the CFP. The purpose of the present study is to propose a new model for cellular manufacturing systems to group parts and machines in dedicated cells using a part-machine incidence matrix to minimize the voids. After identifying the exceptional elements, the machines required for processing the remained operations of corresponding parts which are not processed in the dedicated cells are specified. This results in a new matrix called part family-machine. Then, by clustering the part family-machine incidence matrix, the part families that should be assigned to a specific cell to achieve the highest similarity can be determined. The similarity can be translated to sharing machines required for completing the processes and form new cells called shared cells to minimize the number of exceptional elements and voids. Unlike previous models in which the similarity is considered only in the dedicated cells, in the proposed model, the similarity would be monitored and observed in the entire production process. Due to the complexity of our model, two meta-heuristic algorithms including artificial immune system (AIS) and simulated annealing (SA) are proposed. The efficiency of the algorithms is compared to that of exact solutions. Also, the algorithms are compared regarding the quality of solutions. Finally, according to grouping efficacy measure, SA algorithm has a superior performance in comparison with AIS by spending less CPU time.

Keywords

Albadawi, Z., Bashir, H.A., and Chen, M., (2005). ''A mathematical approach for the formation of manufacturing cells'', Computers & Industrial Engineering, Vol. 48, No. 1, pp. 3–21.
Alimoradi, S., Hematian, M., and Moslehi, G., (2016). ''Robust scheduling of parallel machines considering total flow time'', Computers & Industrial Engineering, Vol. 93, pp. 152–161.
Anvari, M., Mehrabad, M.S., and Barzinpour, F., (2010). ''Machine–part cell formation using a hybrid particle swarm optimization'', The International Journal of Advanced Manufacturing Technology, Vol. 47, No. 5–8, pp. 745–754.
Ayough, A., Tabriz, A.A., and Javani, A., (2015). ''Virtual manufacturing cells scheduling considering lotstreaming and sequence dependent setup times'', Journal of Industrial Engineering and Management Studies, Vol. 2, No. 1, pp. 61–73.
Ballakur, A., and Steudel, H.J., (1987). ''A within-cell utilization based heuristic for designing cellular manufacturing systems'', International Journal of Production Research, Vol. 25, No. 5, pp. 639–665.
Banerjee, I., and Das, P., (2012). ''Group technology based adaptive cell formation using predator–prey genetic algorithm'', Applied Soft Computing, Vol. 12, No. 1, pp. 559–572.
Boctor, F.F., (1991). ''A Jinear formulation of the machine-part cell formation problem'', International Journal of Production Research, Vol. 29, No. 2, pp. 343–356.
Bootaki, B., Mahdavi, I., and Paydar, M.M., (2015). ''New bi-objective robust design-based utilisation towards dynamic cell formation problem with fuzzy random demands'', International Journal of Computer Integrated Manufacturing, Vol. 28, No. 6, pp. 577–592.
Bouaziz, H., Berghida, M., and Lemouari, A., (2020). ''Solving the generalized cubic cell formation problem using discrete flower pollination algorithm'', Expert Systems with Applications, Vol. 150, p. 113345.
Boulif, M., and Atif, K., (2006). ''A new branch-&-bound-enhanced genetic algorithm for the manufacturing cell formation problem'', Computers & Operations Research, Vol. 33, No. 8, pp. 2219–2245.
Brown, J.R., (2015). ''A capacity constrained mathematical programming model for cellular manufacturing with exceptional elements'', Journal of Manufacturing Systems, Vol. 37, pp. 227–232.
Buruk Sahin, Y., and Alpay, S., (2016). ''A metaheuristic approach for a cubic cell formation problem'', Expert Systems with Applications, Vol. 65, pp. 40–51.
Carrie, A.S., (1973). ''Numerical taxonomy applied to group technology and plant layout'', International Journal of Production Research, Vol. 11, No. 4, pp. 399–416.
Chan, H.M., and Milner, D.A., (1982). ''Direct clustering algorithm for group formation in cellular manufacture'', Journal of Manufacturing Systems, Vol. 1, No. 1, pp. 65–75.
Chandrasekharan, M.P., and Rajagopalan, R., (1986a). ''MODROC: an extension of rank order clustering for group technology'', International Journal of Production Research, Vol. 24, No. 5, pp. 1221–1233.
Chandrasekharan, M.P., and Rajagopalan, R., (1986b). ''An ideal seed non-hierarchical clustering algorithm for cellular manufacturing'', International Journal of Production Research, Vol. 24, No. 2, pp. 451–463.
Chandrasekharan, M.P., and Rajagopalan, R., (1989). ''GROUPABILITY: an analysis of the properties of binary data matrices for group technology'', International Journal of Production Research, Vol. 27, No. 6, pp. 1035–1052.
Chen, C.-L., Cotruvo, N.A., and Baek, W., (1995). ''A simulated annealing solution to the cell formation problem'', International Journal of Production Research, Vol. 33, No. 9, pp. 2601–2614.
Chen, S.-J., and Cheng, C.-S., (1995). ''A neural network-based cell formation algorithm in cellular manufacturing'', International Journal of Production Research, Vol. 33, No. 2, pp. 293–318.
Cheng, C.H., Gupta, Y.P., Lee, W.H., and Wong, K.F., (1998). ''A TSP-based heuristic for forming machine groups and part families'', International Journal of Production Research, Vol. 36, No. 5, pp. 1325–1337.
Duran, O., Rodriguez, N., and Consalter, L.A., (2008). ''A PSO-Based Clustering Algorithm for Manufacturing Cell Design'', First International Workshop on Knowledge Discovery and Data Mining (WKDD 2008), IEEE, pp. 72–75.
Elbenani, B., Ferland, J.A., and Bellemare, J., (2012). ''Genetic algorithm and large neighbourhood search to solve the cell formation problem'', Expert Systems with Applications, Vol. 39, No. 3, pp. 2408–2414.
Erenay, B., Suer, G.A., Huang, J., and Maddisetty, S., (2015). ''Comparison of layered cellular manufacturing system design approaches'', Computers & Industrial Engineering, Vol. 85, pp. 346–358.
Farughi, H., Mostafayi, S., and Afrasiabi, A., (2019). ''Bi-objective robust optimization model for configuring cellular manufacturing system with variable machine reliability and parts demand: A real case study'', Journal of Industrial Engineering and Management Studies, Vol. 6, No. 2, pp. 120–146.
Goli, A., Babaee Tirkolaee, E., and Soltani, M., (2019). ''A robust just-in-time flow shop scheduling problem with outsourcing option on subcontractors'', Production & Manufacturing Research, Vol. 7, No. 1, pp. 294–315.
Golpîra, H., and Tirkolaee, E.B., (2019). ''Stable maintenance tasks scheduling: A bi-objective robust optimization model'', Computers & Industrial Engineering, Vol. 137, p. 106007.
Gonçalves, J.F., and Resende, M.G.C., (2004). ''An evolutionary algorithm for manufacturing cell formation'', Computers & Industrial Engineering, Vol. 47, No. 2–3, pp. 247–273.
Heragu, S.S., (1994). ''Group technology and cellular manufacturing'', IEEE Transactions on Systems, Man, and Cybernetics, Vol. 24, No. 2, pp. 203–215.
James, T.L., Brown, E.C., and Keeling, K.B., (2007). ''A hybrid grouping genetic algorithm for the cell formation problem'', Computers & Operations Research, Vol. 34, No. 7, pp. 2059–2079.
Jouzdani, J., Barzinpour, F., Shafia, M.A., and Fathian, M., (2014). ''Applying simulated annealing to a generalized cell formation problem considering alternative routings and machine reliability'', Asia-Pacific Journal of Operational Research, Vol. 31, No. 04, pp. 1–26.
Kia, R., Baboli, A., Javadian, N., Tavakkoli-Moghaddam, R., Kazemi, M., and Khorrami, J., (2012). ''Solving a group layout design model of a dynamic cellular manufacturing system with alternative process routings, lot splitting and flexible reconfiguration by simulated annealing'', Computers & Operations Research, Vol. 39, No. 11, pp. 2642–2658.
Kia, R., Shirazi, H., Javadian, N., and Tavakkoli-Moghaddam, R., (2015). ''Designing group layout of unequal-area facilities in a dynamic cellular manufacturing system with variability in number and shape of cells'', International Journal of Production Research, Vol. 53, No. 11, pp. 3390–3418.
King, J.R., (1980). ''Machine-component grouping in production flow analysis: an approach using a rank order clustering algorithm'', International Journal of Production Research, Vol. 18, No. 2, pp. 213–232.
Kirkpatrick, S., Gelatt, C.D., and Vecchi, M.P., (1983). ''Optimization by Simulated Annealing'', Science, Vol. 220, No. 4598, pp. 671–680.
Kusiak, A., and Cho, M., (1992). ''Similarity coefficient algorithms for solving the group technology problem'', International Journal of Production Research, Vol. 30, No. 11, pp. 2633–2646.
Kusiak, A., and Heragu, S.S., (1987). ''Group technology'', Computers in Industry, Vol. 9, No. 2, pp. 83–91.
Lin, S.-W., and Ying, K.-C., (2013). ''Minimizing makespan in a blocking flowshop using a revised artificial immune system algorithm'', Omega, Vol. 41, No. 2, pp. 383–389.
Mahdavi, I., Aalaei, A., Paydar, M.M., and Solimanpur, M., (2012). ''A new mathematical model for integrating all incidence matrices in multi-dimensional cellular manufacturing system'', Journal of Manufacturing Systems, Vol. 31, No. 2, pp. 214–223.
Mahdavi, I.., Paydar, M.M., Solimanpur, M., and Heidarzade, A., (2009). ''Genetic algorithm approach for solving a cell formation problem in cellular manufacturing'', Expert Systems with Applications, Vol. 36, No. 3, pp. 6598–6604.
Martins, I.C.,, Pinheiro, R.G.S., Protti, F., and Ochi, L.S., (2015). ''A hybrid iterated local search and variable neighborhood descent heuristic applied to the cell formation problem'', Expert Systems with Applications, Vol. 42, No. 22, pp. 8947–8955.
Mehdizadeh, E., Daei Niaki, S.V., and Rahimi, V., (2016). ''A vibration damping optimization algorithm for solving a new multi-objective dynamic cell formation problem with workers training'', Computers & Industrial Engineering, Vol. 101, pp. 35–52.
Mehdizadeh, E., and Rahimi, V., (2016). ''An integrated mathematical model for solving dynamic cell formation problem considering operator assignment and inter/intra cell layouts'', Applied Soft Computing, Vol. 42, pp. 325–341.
Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., and Teller, E., (1953). ''Equation of State Calculations by Fast Computing Machines'', The Journal of Chemical Physics, Vol. 21, No. 6, pp. 1087–1092.
Mosier, C., and Taube, L., (1985). ''Weighted similarity measure heuristics for the group technology machine clustering problem'', Omega, Vol. 13, No. 6, pp. 577–579.
Niakan, F., Baboli, A., Moyaux, T., and Botta-Genoulaz, V., (2016). ''A bi-objective model in sustainable dynamic cell formation problem with skill-based worker assignment'', Journal of Manufacturing Systems, Vol. 38, pp. 46–62.
Noktehdan, A., Karimi, B., and Husseinzadeh Kashan, A., (2010). ''A differential evolution algorithm for the manufacturing cell formation problem using group based operators'', Expert Systems with Applications, Vol. 37, No. 7, pp. 4822–4829.
Onwubolu, G.C., and Mutingi, M., (2001). ''A genetic algorithm approach to cellular manufacturing systems'', Computers & Industrial Engineering, Vol. 39, No. 1–2, pp. 125–144.
Pailla, A., Trindade, A.R., Parada, V., and Ochi, L.S., (2010). ''A numerical comparison between simulated annealing and evolutionary approaches to the cell formation problem'', Expert Systems with Applications, Vol. 37, No. 7, pp. 5476–5483.
Papaioannou, G., and Wilson, J.M., (2010). ''The evolution of cell formation problem methodologies based on recent studies (1997–2008): Review and directions for future research'', European Journal of Operational Research, Vol. 206, No. 3, pp. 509–521.
Paydar, M.M., Mahdavi, I., Khonakdari, S.V., and Solimanpur, M., (2011). ''Developing a mathematical model for cell formation in cellular manufacturing systems'', International Journal of Operational Research, Vol. 11, No. 4, p. 408.
Paydar, M.M., Mahdavi, I., Sharafuddin, I., and Solimanpur, M., (2010). ''Applying simulated annealing for designing cellular manufacturing systems using MDmTSP'', Computers & Industrial Engineering, Vol. 59, No. 4, pp. 929–936.
Paydar, M.M., and Saidi-Mehrabad, M., (2013). ''A hybrid genetic-variable neighborhood search algorithm for the cell formation problem based on grouping efficacy'', Computers & Operations Research, Vol. 40, No. 4, pp. 980–990.
Seifoddini, H., (1989). ''A note on the similarity coefficient method and the problem of improper machine assignment in group technology applications'', International Journal of Production Research, Vol. 27, No. 7, pp. 1161–1165.
Stanfel, L.E., (1985). ''Machine clustering for economic production'', Engineering Costs and Production Economics, Vol. 9, No. 1–3, pp. 73–81.
Suresh Kumar, C., and Chandrasekharan, M.P., (1990). “''Grouping efficacy: a quantitative criterion for goodness of block diagonal forms of binary matrices in group technology'', International Journal of Production Research, Vol. 28, No. 2, pp. 233–243.
Taguchi, G., (1986). Introduction to Quality Engineering : Designing Quality into Products and Processes.
Waghodekar, P.H., and Sahu, S., (1984). ''Machine-component cell formation in group technology: MACE'', International Journal of Production Research, Vol. 22, No. 6, pp. 937–948.
Wemmerlöv, U., and Hyer, N.L., (1989). ''Cellular manufacturing in the U.S. industry: a survey of users'', International Journal of Production Research, Vol. 27, No. 9, pp. 1511–1530.
Wu, T.-H., Chang, C.-C., and Chung, S.-H., (2008). ''A simulated annealing algorithm for manufacturing cell formation problems'', Expert Systems with Applications, Vol. 34, No. 3, pp. 1609–1617.
Xambre, A.R., and Vilarinho, P.M., (2003). ''A simulated annealing approach for manufacturing cell formation with multiple identical machines'', European Journal of Operational Research, Vol. 151, No. 2, pp. 434–446.
Yin, Y., and Yasuda, K., (2006). ‌''Similarity coefficient methods applied to the cell formation problem: A taxonomy and review‌'', International Journal of Production Economics, Vol. 101, No. 2, pp. 329–352.