Mathematical Modeling Approaches to Solve the Line Balancing Problem

Shady Salama, Alyaa Abdelhalim, Amr B. Eltawil

Abstract

The assembly line balancing problem belongs to the class of NP-hard combinatorial optimisation problem. For several decades’ line balancing took attention of researchers who are trying to find the solutions for real world applications. Although tremendous works have been done, the gap still exists between the research and the real problems. This paper provides analysis of about 50 papers that used mathematical modeling in solving line balancing problems. Thereafter, a framework is proposed for future work.

References

  1. Agpak, K. & Gökçen, H., 2007. A chance-constrained approach to stochastic line balancing problem. European Journal of Operational Research, 180(3), pp.1098-1115.
  2. Agrawal, S. & Tiwari, M.K., 2008. A collaborative ant colony algorithm to stochastic mixed-model U-shaped disassembly line balancing and sequencing problem. International Journal of Production Research, 46(6), pp.1405-1429.
  3. Al-e-hashem, S.M., 2009. Mixed model assembly line balancing problem under uncertainty. , 2009. CIE 2009. …. Available at: http://ieeexplore.ieee.org/xpls/ abs_all.jsp?arnumber=5223925 [Accessed September 27, 2016].
  4. Balas, E., Glover, F. & Zionts, S., 1965. An Additive Algorithm for Solving Linear Programs with Zero-One Variables Author(s): Operations Research, 13(4), pp.517-549.
  5. Battaïa, O. & Dolgui, A., 2013. A taxonomy of line balancing problems and their solutionapproaches. International Journal of Production Economics, 142(2), pp.259-277.
  6. Bowman, E.H., 1960. Assembly-Line Balancing by Linear Programming. Operations Research, 8(3), pp.385-389.
  7. Boysen, N., Fliedner, M. & Scholl, A., 2007. A classification of assembly line balancing problems. European Journal of Operational Research, 183(2), pp.674-693.
  8. Carraway, R.L., 1989. A Dynamic Programming Approach to Stochastic Assembly Line Balancing. Management Science, 35(4), pp.459-471. Available at: http://pubsonline.informs.org/doi/abs/10.1287/mnsc.3 5.4.459 [Accessed September 24, 2016].
  9. Dolgui, A. & Battai, O., 2013. Int . J . Production Economics A taxonomy of line balancing problems and their solution approaches. , 142, pp.259-277.
  10. Dong, J. et al., 2014. Balancing and sequencing of stochastic mixed-model assembly U-lines to minimise the expectation of work overload time. International Journal of Production Research, 52(24), pp.7529- 7548. Available at: http://www.tandfonline.com/ doi/abs/10.1080/00207543.2014.944280 [Accessed September 28, 2016].
  11. Esmaeilbeigi, R., Naderi, B. & Charkhgard, P., 2015. The type E simple assembly line balancing problem: A mixed integer linear programming formulation. Computers & Operations Research, 64, pp.168-177. Available at: http://linkinghub.elsevier.com/retrieve /pii/S0305054815001446.
  12. Fattahi, A. et al., 2014. A novel integer programming formulation with logic cuts for the U-shaped assembly line balancing problem. International Journal of Production Research, 52(5), pp.1318-1333. Available at: http://www.tandfonline.com/doi/abs/10.1080/ 00207543.2013.832489 [Accessed September 21, 2016].
  13. Fattahi, P. & Salehi, M., 2009. Sequencing the mixedmodel assembly line to minimize the total utility and idle costs with variable launching interval. The International Journal of Advanced Manufacturing. Available at: http://link.springer.com/article/ 10.1007/s00170-009-2020-0 [Accessed September 25, 2016].
  14. Geoffrion, A.M., 1967. Integer Programming by Implicit Enumeration and Balas' Method. SIAM Review, 9(2), pp.178-190. Available at: http://epubs.siam.org/doi/ abs/10.1137/1009031 [Accessed October 16, 2016].
  15. Gökçen, H. & Agpak, K., 2006. A goal programming approach to simple U-line balancing problem. European Journal of Operational Research, 171(2), pp.577-585.
  16. Gökcen, H. & Erel, E., 1998. Binary Integer Formulation for Mixed-Model Assembly Line Balancing Problem. Computers & Industrial Engineering, 34(2), pp.451- 461. Available at: http://www.sciencedirect.com/ science/article/pii/S0360835297001423.
  17. Guerriero, F. & Miltenburg, J., 2003. The stochastic U-line balancing problem. Naval Research Logistics, 50(1), pp.31-57. Available at: http://doi.wiley.com/10.1002 /nav.10043 [Accessed September 22, 2016].
  18. Gutjahr, A.L. & Nemhauser, G.L., 1964. An Algorithm for the Line Balancing Problem. , (August 2015).
  19. Hamta, N. et al., 2013. A hybrid PSO algorithm for a multiobjective assembly line balancing problem with flexible operation times, sequence-dependent setup times and learning effect. International Journal of Production Economics, 141(1), pp.99-111.
  20. Hazir, Ö. & Dolgui, A., 2013. Assembly line balancing under uncertainty: Robust optimization models and exact solution method. Computers & Industrial Engineering, 65(2), pp.261-267. Available at: http://www.sciencedirect.com/science/article/pii/S036 0835213000934.
  21. Kara, Y., 2008. Line balancing and model sequencing to reduce work overload in mixed-model U-line production environments. Engineering Optimization, 40(7), pp.669-684. Available at: http://www.tandfonline.com/doi/abs/10.1080/0305215 0801982509 [Accessed September 26, 2016].
  22. Kara, Y., Paksoy, T. & Chang, C.-T., 2009. Binary fuzzy goal programming approach to single model straight and U-shaped assembly line balancing. European Journal of Operational Research, 195(2), pp.335-347.
  23. Kara, Y. & Tekin, M., 2009. A mixed integer linear programming formulation for optimal balancing of mixed-model U-lines. International Journal of Production Research, 47(15), pp.4201-4233. Available at: http://www.tandfonline.com/doi/abs/10.1080/ 00207540801905486 [Accessed September 26, 2016].
  24. Kazemi, S.M. et al., 2011. A novel two-stage genetic algorithm for a mixed-model U-line balancing problem with duplicated tasks. The International Journal of Advanced Manufacturing Technology, 55(9-12), pp.1111-1122. Available at: http://link.springer.com/ 10.1007/s00170-010-3120-6 [Accessed September 26, 2016].
  25. Kucukkoc, I. et al., 2015. A mathematical model and artificial bee colony algorithm for the lexicographic bottleneck mixed-model assembly line balancing problem. Journal of Intelligent Manufacturing, pp.1- 13. Available at: http://link.springer.com/10.1007/ s10845-015-1150-5 [Accessed October 24, 2016].
  26. Kucukkoc, I. & Zhang, D.Z., 2014. Mathematical model and agent based solution approach for the simultaneous balancing and sequencing of mixed-model parallel twosided assembly lines. International Journal of Production Economics, 158, pp.314-333.
  27. Miltenburg, G.J. & Wijngaard, J., 1994. The U-line Line Balancing Problem. Management Science, 40(10), pp.1378-1388. Available at: http://pubsonline.informs.org/doi/abs/10.1287/mnsc.4 0.10.1378 [Accessed September 21, 2016].
  28. Miltenburg, J., 2002. Balancing and Scheduling MixedModel U-Shaped Production Lines. International Journal of Flexible Manufacturing Systems, 14(2), pp.119-151. Available at: http://link.springer.com/ 10.1023/A:1014434117888 [Accessed September 26, 2016].
  29. Moodie, C., 1964. A Heuristic Method of Assembly Line Balancing for Assumptions of Constantor Variable Work Element Times. Available at: http://docs.lib.purdue.edu/dissertations/AAI6408691/ [Accessed September 23, 2016].
  30. 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), pp.1359-1370.
  31. Nakade, K., Ohno, K. & George Shanthikumar, J., 1997. Bounds and approximations for cycle times of a Ushaped production line. Operations Research Letters, 21(4), pp.191-200.
  32. Özcan, U., 2010. Balancing stochastic two-sided assembly lines: A chance-constrained, piecewise-linear, mixed integer program and a simulated annealing algorithm. European Journal of Operational Research, 205(1), pp.81-97.
  33. Özcan, U. & Toklu, B., 2009. Multiple-criteria decisionmaking in two-sided assembly line balancing: A goal programming and a fuzzy goal programming models. Computers and Operations Research, 36(6), pp.1955- 1965.
  34. Pastor, R. & Ferrer, L., 2009. An improved mathematical program to solve the simple assembly line balancing problem. International Journal of Production Research, 47(11), pp.2943-2959.
  35. Paternina-Arboleda, C. & Montoya-Torres, J., Mathematical formulation for a mixed-model assembly line balancing problem with stochastic processing times. laccei.org. Available at: http://www.laccei.org/ LACCEI2006-PuertoRico/Copyright Pending/IT240_PaterninaArboleda.pdf [Accessed September 27, 2016].
  36. Patterson, J.H. & Albracht, J.J., 1975. Technical Note-- Assembly-Line Balancing: Zero-One Programming with Fibonacci Search. Operations Research, 23(1), pp.166-172.
  37. 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), pp.1191-1210.
  38. Rabbani, M., Mousavi, Z. & Farrokhi-Asl, H., 2016. Multiobjective metaheuristics for solving a type II robotic mixed-model assembly line balancing problem. Journal of Industrial and Production Engineering, 33(7), pp.472-484. Available at: https://www.tandfonline.com/doi/full/10.1080/216810 15.2015.1126656 [Accessed September 27, 2016].
  39. Ritt, M., Costa, A.M. & Miralles, C., 2016. The assembly line worker assignment and balancing problem with stochastic worker availability. International Journal of Production Research, 54(3), pp.907-922. Available at: http://www.tandfonline.com/doi/full/10.1080/0020754 3.2015.1108534 [Accessed September 25, 2016].
  40. Salveson, M.E., 1955. The assembly line balancing problem. Journal of Industrial Engineering, 6(3), pp.18-25.
  41. 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), pp.489-506.
  42. Sivasankaran, P. & Shahabudeen, P., 2014a. Literature review of assembly line balancing problems. The International Journal of Advanced Manufacturing Technology, 73(9-12), pp.1665-1694. Available at: http://link.springer.com/10.1007/s00170-014-5944-y [Accessed August 20, 2016].
  43. Sivasankaran, P. & Shahabudeen, P., 2014b. Literature review of assembly line balancing problems. The International Journal of Advanced Manufacturing Technology, 73(9-12), pp.1665-1694. Available at: http://link.springer.com/10.1007/s00170-014-5944-y [Accessed September 29, 2016].
  44. Sparling, D. & Miltenburg, J., 1998. The mixed-model Uline balancing problem. International Journal of Production Research, 36(2), pp.485-501.
  45. Talbot, F.B. & Patterson, J.H., 1984. an Integer Programming Algorithm With Network Cuts for Solving the Assembly Line Balancing Problem. Management Science, 30(1), pp.85-99. Available at: http://search.ebscohost.com/login.aspx?direct=true&d b=bth&AN=7357463&site=ehost-live&scope=site.
  46. Thangavelu, S.R. & Shetty, C.M., 1971. Assembly Line Balancing by Zero-One Integer Programming. AIIE Transactions, 3(1), pp.61-68.
  47. Toklu, B. & özcan, U., 2008. A fuzzy goal programming model for the simple U-line balancing problem with multiple objectives. Engineering Optimization, 40(3), pp.191-204. Available at: http://www.tandfonline.com/doi/abs/10.1080/0305215 0701651642 [Accessed September 21, 2016].
  48. Urban, T.L., 1998. Note. Optimal Balancing of U-Shaped Assembly Lines. Management Science, 44(5), pp.738- 741. Available at: http://pubsonline.informs.org/ doi/abs/10.1287/mnsc.44.5.738 [Accessed September 21, 2016].
  49. Urban, T.L. & Chiang, W.C., 2006. An optimal piecewiselinear program for the U-line balancing problem with stochastic task times. European Journal of Operational Research, 168(3), pp.771-782.
  50. 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), pp.1405-1420. Available at: http://www.tandfonline.com/doi/abs/ 10.1080/00207540110116273 [Accessed September 25, 2016].
  51. White, W.W., 1961. Comments on a Paper by Bowman. Operations Research, 9(August 2015), pp.274-276.
  52. Zhao, X. et al., 2016. A genetic algorithm for the multiobjective optimization of mixed-model assembly line based on the mental workload. Engineering Applications of Artificial Intelligence, 47, pp.140-146.
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Paper Citation


in Harvard Style

Salama S., Abdelhalim A. and B. Eltawil A. (2017). Mathematical Modeling Approaches to Solve the Line Balancing Problem . In Proceedings of the 6th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES, ISBN 978-989-758-218-9, pages 401-408. DOI: 10.5220/0006199404010408


in Bibtex Style

@conference{icores17,
author={Shady Salama and Alyaa Abdelhalim and Amr B. Eltawil},
title={Mathematical Modeling Approaches to Solve the Line Balancing Problem},
booktitle={Proceedings of the 6th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},
year={2017},
pages={401-408},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0006199404010408},
isbn={978-989-758-218-9},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 6th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,
TI - Mathematical Modeling Approaches to Solve the Line Balancing Problem
SN - 978-989-758-218-9
AU - Salama S.
AU - Abdelhalim A.
AU - B. Eltawil A.
PY - 2017
SP - 401
EP - 408
DO - 10.5220/0006199404010408