Two-Phase Approach for Machine-Part Grouping Using Non-binary Production Data-Based Part-Machine Incidence Matrix

수리계획법의 활용 분야

  • Published : 2007.05.31

Abstract

In this paper an effective two-phase approach adopting modified p-median mathematical model is proposed for grouping machines and parts in cellular manufacturing(CM). Unlike the conventional methods allowing machines and parts to be improperly assigned to cells and families, the proposed approach seeks to find the proper block diagonal solution where all the machines and parts are properly assigned to their most associated cells and families in term of the actual machine processing and part moves. Phase 1 uses the modified p-median formulation adopting new inter-machine similarity coefficient based on the non-binary production data-based part-machine incidence matrix(PMIM) that reflects both the operation sequences and production volumes for the parts to find machine cells. Phase 2 apollos iterative reassignment procedure to minimize inter-cell part moves and maximize within-cell machine utilization by reassigning improperly assigned machines and parts to their most associated cells and families. Computational experience with the data sets available on literature shows the proposed approach yields good-quality proper block diagonal solution.

Keywords

References

  1. Ben-Arie, D. and P.T. Chang, 'An extension to the p-median group technology algorithm,' Comuters and Operations Research, Vol.21, No.2(1994), pp.119-125 https://doi.org/10.1016/0305-0548(94)90046-9
  2. Chen, S.J. and C.S. Cheng, 'A new neural network-based cell formation algorithm in cellular manufacturing,' International Journal of Production Research, Vol.33, No.2(1995), pp.293-318 https://doi.org/10.1080/00207549508930150
  3. Chu, C.H., 'Recent advances in mathematical programming for cell formation,' Planning, Design, and Analysis of Cellular Manufacturing Systems, Kamrani, A.K. Parsaei, H.R. and Liles, D.H.(Eds.), Elsevier Science B.V. Amsterdam, 1995, pp.1-46
  4. Adenso-Díaz, B., S. Lozano, and I. Eguía, 'Part-machine grouping using weighted similarity coefficients,' Computers and Industrial Engineering, Vol.48 No.2(2005), pp.553-570 https://doi.org/10.1016/j.cie.2003.03.008
  5. Gupta, T. and H. Seifoddini, 'Production data based similarity coefficient for machine- part grouping decisions in the design of a cellular manufacturing system,' International Journal of Production Research, vol.28 No.7(1990), pp.1247-1269 https://doi.org/10.1080/00207549008942791
  6. Harhalakis, G., R. Nagi, and J.M. Proth, 'An efficient heuristic in manufacturing cell formation for group technology,' International Journal of Production Research, Vol. 28, No.1(1990), pp.185-198 https://doi.org/10.1080/00207549008942692
  7. Jayaswal, S. and G.K. Adil, 'Efficient algorithm for cell formation with sequence data, machine replications and alternative process routings,' International Journal of Production Research, Vol.42, No.12(2004), pp.2419-2433 https://doi.org/10.1080/00207540310001652914
  8. Jeon, G.W. and H.R. Leep, 'Forming part families by using genetic algorithm and designing machine cells under demand changes,' Computers and Operations Research, Vol.33, No.1(2006), pp.263-283 https://doi.org/10.1016/j.cor.2005.03.033
  9. Kiang, M.Y., U.R. Kulkarni, and K.Y. Tam, 'Self-organizing map network as an interactive clustering tool an application to group technology,' Decision Support Systems, Vol.15, No.4(1995), pp.351-374 https://doi.org/10.1016/0167-9236(94)00046-1
  10. Kusiak, A., 'The part families problem in flexible manufacturing systems,' Annals of Operations Research, Vol.3(1985), pp.279-300
  11. Kusiak, A., W.J. Boe, and C.H. Cheng, 'Designing cellular manufacturing systems : branch-and-bound and $A^*$ approaches,' IIE Transactions, Vol.25, No.4(1993), pp.46-56 https://doi.org/10.1080/07408179308964303
  12. Kuisak A. and C.H. Chow, 'A branchand- bound algorithm for solving the group technology problem,' Annals of Operations Research, Vol.26(1990), pp.415-431
  13. Lee, H. and A. Garcia-Diaz, 'Network flow procedures for the analysis of cellular manufacturing systems,' IIE Transactions, Vol.28, No.4(1996), pp.333-345 https://doi.org/10.1080/07408179608966280
  14. Lozano, S., D. Canca, F. Guerrero and J.M. Garcia, 'Machine grouping using sequence- based similarity coefficients and neural networks,' Robotics and Computer-Integrated Manufacturing, Vol.17, No.5 (2001), pp.399-404 https://doi.org/10.1016/S0736-5845(01)00015-1
  15. Nair, G.J. and T.T Narendran, 'CASE : A clustering algorithm for cell formation with sequence data,' International Journal of Production Research, Vol.36, No.1 (1998), pp.157-179 https://doi.org/10.1080/002075498193985
  16. Ng, S. M., 'On the characterization and measure of machine cells in group technology,' Operations Research, Vol.44, No.5(1996), pp.735-744 https://doi.org/10.1287/opre.44.5.735
  17. Park, S. and N.C. Suresh, 'Performance of Fuzzy ART neural network and hierarchical clustering for part-machine grouping based on operation sequences,' International Journal of Production Research, Vol.41, No.14(2003), pp.3185-3216 https://doi.org/10.1080/0020754031000110277
  18. Sarker, B.R. and Y. Xu, 'Operation sequences- based cell formation methods: a critical survey,' Production Planning and Control, Vol.9, No.8(1998), pp.771-783 https://doi.org/10.1080/095372898233542
  19. Sarker, B.R. and Y. Xu, 'Designing multi- product lines : job routing in cellular manufacturing systems,' IIE Transactions, Vol.32, No.3(2000), pp.219-235
  20. Seifoddini, H. and M. Djassemi, 'Merits of production volume based similarity coefficient in machine cell formation,' Journal of Manufacturing Systems, Vol.14, No.1(1995), pp.36-44
  21. Seifoddini, H. and C.P. Hsu, 'Comparative study of similarity coefficients and clustering algorithms in cellular manufacturing,' Journal of Manufacturing Systems, Vol.13, No.2(1994), pp.119-127 https://doi.org/10.1016/0278-6125(94)90027-2
  22. Selvam, R.P. and K. N. Balasubramanian, 'Algorithmic grouping of operation sequences,' Engineering Costs and Production Economics, Vol.9, No.1-3(1985), pp.125-134 https://doi.org/10.1016/0167-188X(85)90019-9
  23. Singh, N. and D. Rajamani, Cellular Manufacturing Systems : Design, Planning, and Control, Chapman & Hall. London, 1996
  24. Solimanpur, M., P. Vrat and R. Shankar, 'Ant colony optimization algorithm to the inter-cell layout problem in cellular manufacturing,' European Journal of Operational Research, Vol.157, No.3(2004), pp.592-606 https://doi.org/10.1016/S0377-2217(03)00248-0
  25. Srinivasan, G., T.T. Narendran and B. Mahadevan, 'An assignment model for the part-families problem in group technology,' International Journal of Production Research, Vol.28, No.1(1990), pp.145-152 https://doi.org/10.1080/00207549008942689
  26. Suresh, N.C., J. Slomp and S. Kaparthi, 'Sequence-dependent clustering of parts and machines : a Fuzzy ART neural network approach,' International Journal of Production Research, Vol.37, No.12(1999), pp.2739-2816
  27. Tam, K.Y., 'An operation sequence based similarity coefficients for part families formations,' Journal of Manufacturing Systems, Vol.9, No.1(1990), pp.55-68 https://doi.org/10.1016/0278-6125(90)90069-T
  28. Vakharia, A.J. and U. Wemmerlöv, 'Designing a cellular manufacturing system : a material flow approach based on operation sequences,' IIE Transactions, Vol.22, No.6(1990), pp.84-97 https://doi.org/10.1080/07408179008964161
  29. Venugopal, V. and T.T. Narendran, 'A genetic algorithm approach to the machine- component grouping problem with multiple objectives,' Computers and Industrial Engineering, Vol.22, No.4(1992), pp.469-480 https://doi.org/10.1016/0360-8352(92)90022-C
  30. Viswanathan, S., 'A new approach for solving the p-median problem in group technology,' International Journal of Production Research, Vol.34, No.10(1996), pp.2691-2700 https://doi.org/10.1080/00207549608905053
  31. Wang, J. and C. Roze, 'Formation of machine cells and part families in cellular manufacturing : an experimental study,' International Journal of Production Research, Vol.35, No.5(1997), pp.1259-1286 https://doi.org/10.1080/002075497195317
  32. Wemmerlöve, U. and D.J. Johnson, 'Cellular manufacturing at 46 user plants : implementation experiences and performance improvements,' International Journal of Production Research, Vol.35, No.1(1997), pp.29-49 https://doi.org/10.1080/002075497195966
  33. Won, Y., 'Two-phase approach to GT cell formation using efficient p-median formulations,' International Journal of Production Research, Vol.38, No.7(2000), pp. 1601-1613 https://doi.org/10.1080/002075400188744
  34. Won, Y., 'Effective artificial neural network approach for non-binary incidence matrix-based part-machine grouping,' Korean Operations Research and Management Science Society Journal, Vol.31, No.4(2006), pp69-87
  35. Won, Y. and K.R. Currie, 'Efficient p- median mathematical programming approaches to machine-part grouping in group technology manufacturing,' Engineering Optimization, Vol.36, No.5(2004), pp.555-573 https://doi.org/10.1080/03052150410001696188
  36. Won, Y. and K.R. Currie, 'An effective p-median model considering production factors in machine cell/part family formation,' Journal of Manufacturing Systems, Vol.25, No.1(2006), pp.58-64 https://doi.org/10.1016/S0278-6125(06)80033-6
  37. Won, Y. and K.R. Currie, 'Fuzzy ART/ RRR-RSS : a two-phase neural network nlgorithm for part-machine grouping in cellular manufacturing,' International Journal of Production Research, Vol.45, No.9 (2007), pp.2073-2104 https://doi.org/10.1080/00207540600635227
  38. Won, Y. and K.C. Lee, 'Group technology cell formation considering operation sequences and production volumes,' International Journal of Production Research, Vol.39, No.9(2001), pp.2755-2768 https://doi.org/10.1080/00207540010005060
  39. Wu, W., 'A concurrent approach to cell formation and assignment of identical machines in group technology,' International Journal of Production Research, Vol.36, No.8(1998), pp.2099-2114 https://doi.org/10.1080/002075498192797
  40. Xambre, A.R. and P.M. Vilarinho, 'A simulated annealing approach for manufacturing cell formation with multiple identical machines,' European Journal of Operational Research, Vol.151, No.2(2003), pp.434-446 https://doi.org/10.1016/S0377-2217(02)00836-6
  41. Yin, Y. and K. Yasuda, 'Similarity coefficient methods applied to the cell formation problem : A taxonomy and review,' International Journal of Production Economics, Vol.101, No.2(2006), pp.329-352 https://doi.org/10.1016/j.ijpe.2005.01.014
  42. Yu, J. and B.R. Sarker, 'Directional decomposition heuristic for a linear machine-cell location problem,' European Journal of Operational Research, Vol.149, No.1(2003), pp.142-184 https://doi.org/10.1016/S0377-2217(02)00440-X
  43. Yu, J. and B.R. Sarker, 'A directional decomposition heuristic for one-dimensional, non-equidistant machine-cell location problems,' Computers and Operations Research, Vol.33, No.1(2006), pp.64-92 https://doi.org/10.1016/j.cor.2004.06.003