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A mathematical model and artificial bee colony algorithm for the lexicographic bottleneck mixed-model assembly line balancing problem

  • Ibrahim Kucukkoc
  • Kadir Buyukozkan
  • Sule Itir Satoglu
  • David Z. Zhang
Article

Abstract

Typically, the total number of required workstations are minimised for a given cycle time (this problem is referred to as type-1), or cycle time is minimised for a given number of workstations (this problem is referred to as type-2) in traditional balancing of assembly lines. However, variation in workload distributions of workstations is an important indicator of the quality of the obtained line balance. This needs to be taken into account to improve the reliability of an assembly line against unforeseeable circumstances, such as breakdowns or other failures. For this aim, a new problem, called lexicographic bottleneck mixed-model assembly line balancing problem (LB-MALBP), is presented and formalised. The lexicographic bottleneck objective, which was recently proposed for the simple single-model assembly line system in the literature, is considered for a mixed-model assembly line system. The mathematical model of the LB-MALBP is developed for the first time in the literature and coded in GAMS solver, and optimal solutions are presented for some small scale test problems available in the literature. As it is not possible to get optimal solutions for the large-scale instances, an artificial bee colony algorithm is also implemented for the solution of the LB-MALBP. The solution procedures of the algorithm are explored illustratively. The performance of the algorithm is also assessed using derived well-known test problems in this domain and promising results are observed in reasonable CPU times.

Keywords

Lexicographic bottleneck Assembly line balancing Mixed-model lines Mathematical model Artificial bee colony algorithm 

References

  1. Akgunduz, O. S., & Tunali, S. (2010). An adaptive genetic algorithm approach for the mixed-model assembly line sequencing problem. International Journal of Production Research, 48(17), 5157–5179.CrossRefGoogle Scholar
  2. Akpinar, S., Bayhan, G. M., & Baykasoglu, A. (2013). Hybridizing ant colony optimization via genetic algorithm for mixed-model assembly line balancing problem with sequence dependent setup times between tasks. Applied Soft Computing, 13(1), 574–589.CrossRefGoogle Scholar
  3. Akpinar, S., & Baykasoglu, A. (2014). Modeling and solving mixed-model assembly line balancing problem with setups. Part I: A mixed integer linear programming model. Journal of Manufacturing Systems, 33(1), 177–187.CrossRefGoogle Scholar
  4. Askin, R. G., & Zhou, M. (1997). A parallel station heuristic for the mixed-model production line balancing problem. International Journal of Production Research, 35(11), 3095–3106.CrossRefGoogle Scholar
  5. Battaïa, O., & Dolgui, A. (2013). A taxonomy of line balancing problems and their solution approaches. International Journal of Production Economics, 142(2), 259–277.CrossRefGoogle Scholar
  6. Battini, D., Faccio, M., Ferrari, E., Persona, A., & Sgarbossa, F. (2007). Design configuration for a mixed-model assembly system in case of low product demand. International Journal of Advanced Manufacturing Technology, 34(1–2), 188–200.CrossRefGoogle Scholar
  7. Baybars, I. (1986). A survey of exact algorithms for the simple assembly line balancing problem. Management Science, 32(8), 909–932.CrossRefGoogle Scholar
  8. Baykasoglu, A., & Dereli, T. (2009). Simple and U-type assembly line balancing by using an ant colony based algorithm. Mathematical & Computational Applications, 14(1), 1–12.Google Scholar
  9. Becker, C., & Scholl, A. (2006). A survey on problems and methods in generalized assembly line balancing. European Journal of Operational Research, 168(3), 694–715.CrossRefGoogle Scholar
  10. Boysen, N., Fliedner, M., & Scholl, A. (2007). A classification of assembly line balancing problems. European Journal of Operational Research, 183(2), 674–693.CrossRefGoogle Scholar
  11. Chutima, P., & Chimklai, P. (2012). Multi-objective two-sided mixed-model assembly line balancing using particle swarm optimisation with negative knowledge. Computers & Industrial Engineering, 62(1), 39–55.CrossRefGoogle Scholar
  12. Dueck, G. (1993). New optimization heuristics. Journal of Computational Physics, 104(1), 86–92.CrossRefGoogle Scholar
  13. Emde, S., Boysen, N., & Scholl, A. (2010). Balancing mixed-model assembly lines: A computational evaluation of objectives to smoothen workload. International Journal of Production Research, 48(11), 3173–3191.CrossRefGoogle Scholar
  14. García-Villoria, A., & Pastor, R. (2013). Erratum to “A solution procedure for type E simple assembly line balancing problem”. Computers & Industrial Engineering, 66(1), 201–202.CrossRefGoogle Scholar
  15. Ghosh, S., & Gagnon, R. J. (1989). A comprehensive literature review and analysis of the design, balancing and scheduling of assembly systems. International Journal of Production Research, 27(4), 637–670.CrossRefGoogle Scholar
  16. Gokcen, H., & Erel, E. (1997). A goal programming approach to mixed-model assembly line balancing problem. International Journal of Production Economics, 48(2), 177–185.CrossRefGoogle Scholar
  17. Gökçen, H., & Erel, E. (1998). Binary integer formulation for mixed-model assembly line balancing problem. Computers & Industrial Engineering, 34(2), 451–461.CrossRefGoogle Scholar
  18. Hackman, S. T., Magazine, M. J., & Wee, T. S. (1989). Fast, effective algorithms for simple assembly line balancing problems. Operations Research, 37(6), 916–924.CrossRefGoogle Scholar
  19. Hamta, N., Ghomi, S. M. T. F., Jolai, F., & Shirazi, M. A. (2013). A hybrid PSO algorithm for a multi-objective assembly line balancing problem with flexible operation times, sequence-dependent setup times and learning effect. International Journal of Production Economics, 141(1), 99–111.CrossRefGoogle Scholar
  20. Hamzadayi, A., & Yildiz, G. (2012). A genetic algorithm based approach for simultaneously balancing and sequencing of mixed-model U-lines with parallel workstations and zoning constraints. Computers & Industrial Engineering, 62(1), 206–215.CrossRefGoogle Scholar
  21. Haq, A. N., Rengarajan, K., & Jayaprakash, J. (2006). A hybrid genetic algorithm approach to mixed-model assembly line balancing. International Journal of Advanced Manufacturing Technology, 28(3–4), 337–341.Google Scholar
  22. Hwang, R., & Katayama, H. (2009). A multi-decision genetic approach for workload balancing of mixed-model U-shaped assembly line systems. International Journal of Production Research, 47(14), 3797–3822.CrossRefGoogle Scholar
  23. Hwang, R., & Katayama, H. (2010). Integrated procedure of balancing and sequencing for mixed-model assembly lines: A multi-objective evolutionary approach. International Journal of Production Research, 48(21), 6417–6441.CrossRefGoogle Scholar
  24. Kara, Y., Ozcan, U., & Peker, A. (2007a). An approach for balancing and sequencing mixed-model JIT U-lines. International Journal of Advanced Manufacturing Technology, 32(11–12), 1218–1231.CrossRefGoogle Scholar
  25. Kara, Y., Ozcan, U., & Peker, A. (2007b). Balancing and sequencing mixed-model just-in-time U-lines with multiple objectives. Applied Mathematics and Computation, 184(2), 566–588.CrossRefGoogle Scholar
  26. Kara, Y., & Tekin, M. (2009). A mixed integer linear programming formulation for optimal balancing of mixed-model U-lines. International Journal of ProductionResearch, 47(15), 4201–4233.CrossRefGoogle Scholar
  27. Karaboga, D. (2005). An idea based on honey bee swarm for numerical optimization. Technical report TR06. In Computer Engineering Department, Engineering Faculty, Erciyes University, Turkey.Google Scholar
  28. Karaboga, D., & Basturk, B. (2008). On the performance of artificial bee colony (ABC) algorithm. Applied Soft Computing, 8(1), 687–697.CrossRefGoogle Scholar
  29. Kucukkoc, I., Karaoglan, A. D., & Yaman, R. (2013). Using response surface design to determine the optimal parameters of genetic algorithm and a case study. International Journal of Production Research, 51(17), 5039–5054. doi: 10.1080/00207543.2013.784411.CrossRefGoogle Scholar
  30. Kucukkoc, I., & Zhang, D. Z. (2014). Mathematical model and agent based solution approach for the simultaneous balancing and sequencing of mixed-model parallel two-sided assembly lines. International Journal of Production Economics, 158, 314–333. doi: 10.1016/j.ijpe.2014.08.010.CrossRefGoogle Scholar
  31. Kucukkoc, I., & Zhang, D. Z. (2014b). Simultaneous balancing and sequencing of mixed-model parallel two-sided assembly lines. International Journal of Production Research, 52(12), 3665–3687. doi: 10.1080/00207543.2013.879618.CrossRefGoogle Scholar
  32. Kucukkoc, I., & Zhang, D. Z. (2015). Balancing of parallel U-shaped assembly lines. Computers and Operations Research, 64, 233–244. doi: 10.1016/j.cor.2015.05.014.CrossRefGoogle Scholar
  33. Kucukkoc, I., & Zhang, D. Z. (2015b). A mathematical model and genetic algorithm-based approach for parallel two-sided assembly line balancing problem. Production Planning and Control, 26(11), 874–894. doi: 10.1080/09537287.2014.994685.CrossRefGoogle Scholar
  34. Kucukkoc, I., & Zhang, D. Z. (2015c). Type-E parallel two-sided assembly line balancing problem: Mathematical model and ant colony optimisation based approach with optimised parameters. Computers and Industrial Engineering, 84, 56–69. doi: 10.1016/j.cie.2014.12.037.CrossRefGoogle Scholar
  35. Kucukkoc, I., & Zhang, D. Z. (2015d). Integrating ant colony and genetic algorithms in the balancing and scheduling of complex assembly lines. The International Journal of Advanced Manufacturing Technology. doi: 10.1007/s00170-015-7320-y.
  36. Liao, L. M., Huang, C. J., & Huang, J. H. (2012). Applying multi-agent approach to mixed-model assembly line balancing. In Proceedings of the IEEE ICMIT.Google Scholar
  37. Liu, S. B., Ong, H. L., & Huang, H. C. (2004). A bidirectional heuristic for stochastic assembly line balancing Type II problem. The International Journal of Advanced Manufacturing Technology, 25(1–2), 71–77.Google Scholar
  38. Manavizadeh, N., Hosseini, N. S., Rabbani, M., & Jolai, F. (2013). A simulated annealing algorithm for a mixed model assembly U-line balancing type-I problem considering human efficiency and just-in-time approach. Computers & Industrial Engineering, 64(2), 669–685.CrossRefGoogle Scholar
  39. Manavizadeh, N., Rabbani, M., Moshtaghi, D., & Jolai, F. (2012). Mixed-model assembly line balancing in the make-to-order and stochastic environment using multi-objective evolutionary algorithms. Expert Systems with Applications, 39(15), 12026–12031.CrossRefGoogle Scholar
  40. McMullen, P. R., & Tarasewich, P. (2003). Using ant techniques to solve the assembly line balancing problem. IIE Transactions, 35(7), 605–617.CrossRefGoogle Scholar
  41. Mosadegh, H., Zandieh, M., & Ghomi, S. M. T. F. (2012). Simultaneous solving of balancing and sequencing problems with station-dependent assembly times for mixed-model assembly lines. Applied Soft Computing, 12(4), 1359–1370.CrossRefGoogle Scholar
  42. Ozbakir, L., & Tapkan, P. (2011). Bee colony intelligence in zone constrained two-sided assembly line balancing problem. Expert Systems with Applications, 38(9), 11947–11957.CrossRefGoogle Scholar
  43. Ozcan, U., Kellegoz, T., & Toklu, B. (2011). A genetic algorithm for the stochastic mixed-model U-line balancing and sequencing problem. International Journal of Production Research, 49(6), 1605–1626.CrossRefGoogle Scholar
  44. Ozcan, U., & Toklu, B. (2009). Balancing of mixed-model two-sided assembly lines. Computers & Industrial Engineering, 57(1), 217–227.CrossRefGoogle Scholar
  45. Pastor, R. (2011). LB-ALBP: The lexicographic bottleneck assembly line balancing problem. International Journal of Production Research, 49(8), 2425–2442.CrossRefGoogle Scholar
  46. Pastor, R., Chueca, I., & García-Villoria, A. (2012). A heuristic procedure for solving the lexicographic bottleneck assembly line balancing problem (LB-ALBP). International Journal of Production Research, 50(7), 1862–1876.CrossRefGoogle Scholar
  47. Pastor, R., García-Villoria, A., Laguna, M., & Martí, R. (2015). Metaheuristic procedures for the lexicographic bottleneck assembly line balancing problem. Journal of the Operational Research Society. doi: 10.1057/jors.2014.138.
  48. Rabbani, M., Moghaddam, M., & Manavizadeh, N. (2012). Balancing of mixed-model two-sided assembly lines with multiple U-shaped layout. International Journal of Advanced Manufacturing Technology, 59(9–12), 1191–1210.CrossRefGoogle Scholar
  49. Rashedi, E., Nezamabadi-pour, H., & Saryazdi, S. (2009). GSA: A gravitational search algorithm. Information Sciences, 179(13), 2232–2248.CrossRefGoogle Scholar
  50. Rekiek, B., Dolgui, A., Delchambre, A., & Bratcu, A. (2002). State of art of optimization methods for assembly line design. Annual Reviews in Control, 26, 163–174.CrossRefGoogle Scholar
  51. Satoglu, S. I., & Ethem Sahin, I. (2012). Design of a just-in-time periodic material supply system for the assembly lines and an application in electronics industry. The International Journal of Advanced Manufacturing Technology, 65(1–4), 319–332.Google Scholar
  52. Simaria, A. S., & Vilarinho, P. M. (2009). 2-ANTBAL: An ant colony optimisation algorithm for balancing two-sided assembly lines. Computers & Industrial Engineering, 56(2), 489–506.CrossRefGoogle Scholar
  53. Simaria, A. S., & Vilarinho, P. M. (2004). A genetic algorithm based approach to the mixed-model assembly line balancing problem of type II. Computers & Industrial Engineering, 47(4), 391–407.CrossRefGoogle Scholar
  54. Sivasankaran, P., & Shahabudeen, P. (2014). Literature review of assembly line balancing problems. The International Journal of Advanced Manufacturing Technology, 73(9–12), 1665–1694.CrossRefGoogle Scholar
  55. Tapkan, P., Ozbakir, L., & Baykasoglu, A. (2012a). Bees algorithm for constrained fuzzy multi-objective two-sided assembly line balancing problem. Optimization Letters, 6(6), 1039–1049.CrossRefGoogle Scholar
  56. Tapkan, P., Ozbakir, L., & Baykasoglu, A. (2012b). Modeling and solving constrained two-sided assembly line balancing problem via bee algorithms. Applied Soft Computing, 12(11), 3343–3355.CrossRefGoogle Scholar
  57. Thomopoulos, N. T. (1967). Line balancing-sequencing for mixed-model assembly. Management Science, 14(2), 59–75.CrossRefGoogle Scholar
  58. Tiacci, L. (2015). Simultaneous balancing and buffer allocation decisions for the design of mixed-model assembly lines with parallel workstations and stochastic task times. International Journal of Production Economics, 162, 201–215.CrossRefGoogle Scholar
  59. Venkata Rao, R. (2016). Jaya: A simple and new optimization algorithm for solving constrained and unconstrained optimization problems. International Journal of Industrial Engineering Computations, 7, 19–34. doi: 10.5267/j.ijiec.2015.8.004.CrossRefGoogle Scholar
  60. Vilarinho, P. M., & Simaria, A. S. (2002). A two-stage heuristic method for balancing mixed-model assembly lines with parallel workstations. International Journal of Production Research, 40(6), 1405–1420.CrossRefGoogle Scholar
  61. Wei, N.-C., & Chao, I. M. (2011). A solution procedure for type E simple assembly line balancing problem. Computers & Industrial Engineering, 61(3), 824–830.CrossRefGoogle Scholar
  62. Xu, W., & Xiao, T. (2011). Strategic robust mixed model assembly line balancing based on scenario planning. Tsinghua Science and Technology, 16(3), 308–314.CrossRefGoogle Scholar
  63. Yagmahan, B. (2011). Mixed-model assembly line balancing using a multi-objective ant colony optimization approach. Expert Systems with Applications, 38(10), 12453–12461.CrossRefGoogle Scholar
  64. Yoosefelahi, A., Aminnayeri, M., Mosadegh, H., & Davari Ardakani, H. (2012). Type II robotic assembly line balancing problem: An evolution strategies algorithm for a multi-objective model. Journal of Manufacturing Systems, 31(2), 139–151.CrossRefGoogle Scholar
  65. Zhang, D. Z., & Kucukkoc, I. (2013). Balancing mixed-model parallel two-sided assembly lines. In L. Amodeo, A. Dolgui, & F. Yalaoui Proceedings of 2013 international conference on industrial engineering and systems management, IEEE–IESM 2013, art. no. 6761429, 28–30 October, Rabat, Morocco (pp. 391–401).Google Scholar
  66. Zhang, W. Q., & Gen, M. (2011). An efficient multiobjective genetic algorithm for mixed-model assembly line balancing problem considering demand ratio-based cycle time. Journal of Intelligent Manufacturing, 22(3), 367–378.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.College of Engineering, Mathematics and Physical SciencesUniversity of ExeterExeterEngland, UK
  2. 2.Department of Industrial Engineering, Faculty of Engineering and ArchitectureBalikesir UniversityBalıkesirTurkey
  3. 3.Industrial Engineering DepartmentIstanbul Technical UniversityIstanbulTurkey
  4. 4.Department of Industrial Engineering, Faculty of EngineeringKaradeniz Technical UniversityTrabzonTurkey

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