A Grouping Genetic Algorithm for heuristically solving the cell formation problem

1. A Grouping Genetic Algorithm for heuristically solving the cell formation problem Teerawut Tunnukij Christian Hicks Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne

2. Components of GAs • Problems of the classical GAs for solving the cell formation problem Goal Performance & benefits of the proposed GGA General structure & components of the developed GGA Benefits of GT/CM to facilities layout design • General problems of clustering methods • Suitable methods for the solutions Road Map Comparisons & performance Developed GGA Clustering methods GGAs GAs GT/CM Facilities layout design Start Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne

3. The facilities layout design Job Assignment Select machines for each operation and specify operation sequences Cell Formation Group machines into cells Layout Design Assign cells within plants and machines within cells Transportation System Design Design aisle structure and select material handling equipment Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne

4. have been used for identifying Manufacturing cells Based upon Group Technology GT has been applied to manufacturing systems known as Cellular Manufacturing (CM). Group Technology & Cellular Manufacturing Clustering Methods A philosophy that aims to exploit similarities and achieve efficiencies by grouping. Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne

5. T T T CG CG T T T M M M T T T T SG SG M D D D M M D D D SG CG CG D M M SG D D D Manufacturing Layout Process (Functional) Layout Group (Cellular) Layout A cluster or cell Like resources placed together Resources to produce like products placed together Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne

6. Reduced Manufacturing Costs The benefits of CM • Main benefits • Reduced throughput time • Reduced work in progress • Improved material flows • Others • Reduced inventory • Improved use of space • Improved team work • Reduced waste • Increased flexibility Cellular Manufacturing Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne

7. Part family grouping Can be classified into Machine grouping Machine-part grouping Clustering Methods Form part families and then group machines into cells. A large number of clustering methods have been developed Form machine cells based upon similarities in part routing and then allocate parts to cells. Form part families and machine cells simultaneously. Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne

8. Clustering Methods Part family grouping Machine grouping Similarity coefficient- based Methods Classification & Coding Graph theoretic Mathematical Programming- based Methods Meta-heuristic Methods Heuristic Methods Machine-part grouping Machine-Part incidence matrix-based Methods • Most of these methods have exploited the machine-part matrix as the initial information to identify potential manufacturing cells. Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne

9. A machine-part incidence matrix Exceptional elements Parts Parts Machines Machines (a) the original matrix (b) a rearranged matrix into block-diagonal forms Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne

10. Meta-heuristic methods • Good methods for the solution • SA, TS, GAs General problems of clustering methods Conventional methods do not always produce a desirable solution. There are many ‘exceptional elements’ (machines & parts that cannot be assigned to cells). The cell formation problem has been shown to be a non-deterministic polynomial (NP) complete problem. Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne

11. Genetic Algorithms (GAs) • GAs are one of the meta-heuristic algorithms. They are stochastic search techniques for approximating optimal solutions within complex search spaces. • The technique is based upon the mechanics of natural genetics and selection. • The basic idea derived from an analogy with biological evolution, in which the fitness of individual determines its ability to survive and reproduce, known as ‘the survival of the fittest’. Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne

12. GAs: The main components 1. Genetic representation 5. Genetic operators 2. Method for generating the initial population 6. Mechanism for creating successive generations GAs 3. Evaluation function 7. Stopping Criteria 4. Reproduction selection scheme 8. GA parameter settings Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne

13. The general chromosome representation 6 parts (or machines) A potential solution Chromosome: Cell 1: 1,2,6 Cell 2: 3,5 Cell 3: 4 Cell number GAs: The cell formation problem • Venugopal and Narendran (1992) were the first researchers to apply GAs to the cell formation problem. Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne

14. This repetition problem • increases the size of the search space; • reduces the effectiveness of the GAs. All chromosomes represent the same solution GAs: The problem of the classical GAs • The standard gene encoding scheme includes significant redundancy when representing a grouping problem (Falkenauer 1998) Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne

15. Grouping Genetic Algorithms (GGAs) • The GGA, introduced by Falkenauer (1998), is a specialised GA tool that has been adapted to suit and handle the structure of grouping problems. • The GGA differs from the classical GAs in two important aspects:1. The special gene encoding scheme;2. The special genetic operators. • De Lit et al. (2000) first applied the GGA to solve the cell formation problem with the fixed maximum cell size. Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne

16. Genetic Operation Crossover operation Parent 1 Offspring 1 Parent 2 Offspring 2 Mutation operation Offspring 1 Parent 1 Repair Process Check & remove empty cells Check no. of cells 2≤C≤min(M-1,P-1) Check & replace duplicate cell no. Check & relocate unassigned parts & machines The developed GGA: The general structure 1 2 4 3 Encode Genes Generate Population Population Start Chromosome Random selection Integer representing a cell number Randomly combine genes with a repair process Chromosome Stop Create population for the next generation Number of generation Yes Terminate? No 7 Chromosome 4.1 Chromosome selection 6 5 Roulette Wheel Evaluate Fitness Grouping efficacy Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne

17. the performance of the GGA proposed by Yasuda, et al. (2005) the performance of the developed GGA The analysis of performance A simple CFP (a) The 5x8 original matrix (b) The 5x8 matrix after clustered Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne

18. The analysis of performance Comparisons of five clustering algorithms • CR1-CR7 obtained from Chandrasekharan and Rajagopalan (1989) • KN1 obtained from King and Nakornchai (1982) Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne

19. The analysis of performance Grouping efficacy Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne

20. Conclusions • The developed GGA including a repair process was developed for solving the CFP withoutthe predetermination of the No. of manufacturing cells and the No. of machines within the cell. • The developed GGA was applied to well-known data sets from the literature and was compared to other methods. The results show the developed GGA is effective, performs very well, and outperforms other selected methods in most cases. • The designed parameter experiment suggests that the large no. of population size have more chance to obtain the better solution, and using the range 0.6-0.7 for probability of crossover and the range 0.2-0.3 for probability of mutation tends to produce the better solution. Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne

21. Further Work • Develop the proposed GGA to be able to consider important parameters such as operation sequences and others. • Apply the developed GGA to a data set obtained from a collaborating company. Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne

22. Thank you Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne

23. References Aytug, H., Khouja, M. and Vergara, F. E., 2003, Use of genetic algorithms to solve production and operations management problems: A review, International Journal of Production Research, 41(17), 3955-4009. Brown, E. C. and Sumichrast, R. T., 2001, CF-GGA: A grouping genetic algorithm for the cell formation problem, International Journal of Production Research, 39(16), 3651-3669. 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, 27(6), 1035-1052. Cheng, C. H., Gupta, Y. P., Lee, W. H. and Wong, K. F., 1998, TSP-based heuristic for forming machine groups and part families, International Journal of Production Research, 36(5), 1325-1337. De Lit, P., Falkenauer, E. and Delchambre, A., 2000, Grouping genetic algorithms: An efficient method to solve the cell formation problem, Mathematics and Computers in Simulation, 51(3-4), 257-271. Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne

24. References Dimopoulos, C. and Zalzala, A. M. S., 2000, Recent developments in evolutionary computation for manufacturing optimization: Problems, solutions, and comparisons, IEEE Transactions on Evolutionary Computation, 4(2), 93-113. Falkenauer, E., 1998, Genetic Algorithms and Grouping Problems (New York: John Wiley & Sons). Gallagher, C. C. and Knight, W. A., 1973, Group Technology (London: Gutterworth). Gallagher, C. C. and Knight, W. A., 1986, Group Technology Production Methods in Manufacture (New York: Wiley). Hyer, N. L. and Wemmerlov, U., 1984, Group Technology and Productivity, Harvard Business Review, 62(4), 140-149. King, J. R. and Nakornchai, V., 1982, Machine-Component Group Formation in Group Technology - Review and Extension, International Journal of Production Research, 20(2), 117-133. Kumar, C. S. 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, 28(2), 233-243. Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne

25. References Srinivasan, G. and Narendran, T. T., 1991, GRAFICS. A nonhierarchical clustering algorithm for group technology, International Journal of Production Research, 29(3), 463-478. Venugopal, V. and Narendran, T. T., 1992, Genetic algorithm approach to the machine-component grouping problem with multiple objectives, Computers & Industrial Engineering, 22(4), 469-480. Wemmerlov, U. and Hyer, N. L., 1989, Cellular manufacturing in the US industry: a survey of users, International Journal of Production Research, 27(9), 1511-1530. Wu, Y., 1999, Computer aided design of cellular manufacturing layout, Ph.D. Thesis, School of Engineering and Applied Science, University of Durham. Yasuda, K., Hu, L. and Yin, Y., 2005, A grouping genetic algorithm for the multi-objective cell formation problem, International Journal of Production Research, 43(4), 829-853. Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne