# Balancing two-sided U-type assembly lines using modified particle swarm optimization algorithm

## Abstract

In this paper, a new two-sided U-type assembly line balancing (TUALB) procedure and a new algorithm based on the particle swarm optimization algorithm to solve the TUALB problem are proposed. The proposed approach minimizes the number of stations for a given cycle time as the primary objective and it minimizes the number of positions as a secondary objective. The proposed approach is illustrated with an example problem. In order to evaluate the efficiency of the proposed algorithm, the test problems available in the literature are used. The experimental results show that the proposed approach performs well.

## Keywords

Two-sided assembly line balancing U-type assembly lines Particle swarm optimization## Mathematics Subject Classification

90B30 90C59## Notes

### Acknowledgments

The authors would like to thank the referees for their careful review of the paper and their helpful comments and suggestions which greatly improved the paper. This research was supported by the Erciyes University Scientific Research Projects Grand Number SDK-2013-4636.

### Compliance with ethical standards

### Conflict of interest

No potential conflict of interest was reported by the authors.

## References

- Aghajani M, Ghodsi R, Javadi B (2014) Balancing of robotic mixed-model two-sided assembly line with robot setup times. Int J Adv Manuf Technol. doi: 10.1007/s00170-014-5945-x Google Scholar
- Ağpak K, Yegül MF, Gökçen H (2012) Two-sided U-type assembly line balancing problem. Int J Prod Res 50(18):5035–5047CrossRefGoogle Scholar
- Aigbedo H, Monden Y (1997) A parametric procedure for multi-criterion sequence scheduling for just-in-time mixed-model assembly lines. Int J Prod Res 35:2543–2564CrossRefGoogle Scholar
- Bartholdi JJ (1993) Balancing two-sided assembly lines: a case study. Int J Prod Res 31:2447–2461CrossRefGoogle Scholar
- Battaia O, Dolgui A (2013) A taxonomy of line balancing problems and their solution approaches. Int J Prod Econ 142:259–277CrossRefGoogle Scholar
- Baybars I (1986) A survey of exact algorithms for the simple line balancing problem. Manag Sci 32:909–932CrossRefGoogle Scholar
- Baykasoğlu A, Dereli T (2008) Two-sided assembly line balancing using an ant-colony-based heuristic. Int J Adv Manuf Technol 36:582–588CrossRefGoogle Scholar
- Becker C, Scholl A (2006) A survey on problems and methods in generalized assembly line balancing. Eur J Oper Res 168:694–715CrossRefGoogle Scholar
- Boysen N, Fliedner M, Scholl A (2007) A classification of assembly line balancing problems. Eur J Oper Res 183:674–693CrossRefGoogle Scholar
- Chutima P, Chimklai P (2012) Multi-objective two-sided mixed-model assembly line balancing using particle swarm optimisation with negative knowledge. Comput Ind Eng 62(1):39–55CrossRefGoogle Scholar
- Chutima P, Jitmetta K (2013) Adaptive biogeography-based optimisation for two-sided mixed-model assembly line sequencing problems. Int J Oper Res 16(4):390–420CrossRefGoogle Scholar
- Chutima P, Naruemitwong W (2014) A Pareto biogeography-based optimisation for multi-objective two-sided assembly line sequencing problems with a learning effect. Comput Ind Eng 69(1):89–104CrossRefGoogle Scholar
- Erel E, Sarin SC (1998) A survey of the assembly line balancing procedures. Prod Plan Control 9:414–434CrossRefGoogle Scholar
- Ghosh S, Gagnon J (1989) A comprehensive literature review and analysis of the design, balancing and scheduling of assembly systems. Int J Prod Res 27:637–670CrossRefGoogle Scholar
- Gutjahr AL, Nemhauser GL (1964) An algorithm for the line balancing problem. Manage Sci 11(2):308–315CrossRefGoogle Scholar
- Hu X-F, Wu E-W, Jin Y (2008) A station-oriented enumerative algorithm for two-sided assembly line balancing. Eur J Oper Res 186:435–440CrossRefGoogle Scholar
- Kennedy J, Eberhart RC (1995) Particle swarm optimization. In: IEEE International Conferenceon Neural Networks, Perth, Australia, pp 1942–1948Google Scholar
- Kennedy J, Eberhart RC (1997) A discrete binary version of the particle swarm optimization. Proceedings of the conference on systems, man, and cybernetics SMC97, pp 4104–4108Google Scholar
- Kennedy J, Eberhart RC, Shi Y (2001) Swarm intelligence. Morgan Kaufman, San FranciscoGoogle Scholar
- Khorasanian D, Hejazi SR, Moslehi G (2013) Two-sided assembly line balancing considering the relationships between tasks. Comput Ind Eng 66(4):1096–1105CrossRefGoogle Scholar
- Kim YK, Kim Y, Kim YJ (2000) Two-sided assembly line balancing: a genetic algorithm approach. Prod Plan Control 11:44–53CrossRefGoogle Scholar
- Kim YK, Song WS, Kim JH (2009) A mathematical model and a genetic algorithm for two-sided assembly line balancing. Comput Oper Res 36:853–865CrossRefGoogle Scholar
- Kucukkoc I, Zhang DZ (2014) Simultaneous balancing and sequencing of mixed-model parallel two-sided assembly lines. Int J Prod Res 52(12):3665–3687CrossRefGoogle Scholar
- Lapierre SD, Ruiz AB (2004) Balancing assembly lines: an industrial case study. J Oper Res Soc 55:589–597CrossRefGoogle Scholar
- Lee TO, Kim Y, Kim YK (2001) Two-sided assembly line balancing to maximize work relatedness and slackness. Comput Ind Eng 40:273–292CrossRefGoogle Scholar
- Li D, Zhang C, Shao X, Lin W (2014) A multi-objective TLBO algorithm for balancing two-sided assembly line with multiple constraints. J Intell Manuf. doi: 10.1007/s10845-014-0919-2 Google Scholar
- Liao CJ, Tseng CT, Luarn P (2007) A discrete version of particle swarm optimization for flowshop scheduling problems. Comput Oper Res 34:3099–3111CrossRefGoogle Scholar
- Miltenburg J (1998) Balancing U-lines in a multiple U-line facility. Eur J Oper Res 109:1–23CrossRefGoogle Scholar
- Özbakir L, Tapkan P (2010) Balancing fuzzy multi-objective two-sided assembly lines via Bees Algorithm. J Intell Fuzzy Syst 21(5):317–329Google Scholar
- Özbakir L, Tapkan P (2011) Bee colony intelligence in zone constrained two-sided assembly line balancing problem. Expert Syst Appl 38(9):11947–11957CrossRefGoogle Scholar
- Özcan U, Toklu B (2009a) Multiple-criteria decision-making in two-sided assembly line balancing: a goal programming and a fuzzy goal programming models. Comput Oper Res 36:1955–1965CrossRefGoogle Scholar
- Özcan U, Toklu B (2009b) A tabu search algorithm for two-sided assembly line balancing. Int J Adv Manuf Technol 43:822–829CrossRefGoogle Scholar
- Özcan U, Toklu B (2009c) Balancing of mixed-model two-sided assembly lines. Comput Ind Eng 57:217–227CrossRefGoogle Scholar
- Özcan U (2010) Balancing stochastic two-sided assembly lines: a chance-constrained, piecewise-linear, mixed integer program and a simulated annealing algorithm. Eur J Oper Res 205(1):81–97CrossRefGoogle Scholar
- Özcan U, Gökcen H, Toklu B (2010) Balancing parallel two-sided assembly lines. Int J Prod Res 48(16):4767–4784CrossRefGoogle Scholar
- Özcan U, Toklu B (2010) Balancing two-sided assembly lines with sequence-dependent setup times. Int J Prod Res 48(18):5363–5383CrossRefGoogle Scholar
- Purnomo HD, Wee H-M, Rau H (2013) Two-sided assembly lines balancing with assignment restrictions. Math Comput Model 57(1–2):189–199CrossRefGoogle Scholar
- Rabbani M, Moghaddam M, Manavizadeh N (2012) Balancing of mixed-model two-sided assembly lines with multiple U-shaped layout. Int J Adv Manuf Technol 59(9–12):1191–1210CrossRefGoogle Scholar
- Roshani A, Fattahi P, Roshani A, Salehi M, Roshani A (2012) Cost-oriented two-sided assembly line balancing problem: a simulated annealing approach. Int J Comput Integr Manuf 25(8):689–715CrossRefGoogle Scholar
- Shi Y, Eberhart RC (1998) A modified particle swarm optimizer. Proceedings of the IEEE congress on evolutionary computation, USA, pp 69–73Google Scholar
- Shi Y, Eberhart RC (1999) Empirical study of particle swarm optimization. Proceedings of the IEEE congress on evolutionary computation, IEEE Press, pp 1945–1950Google Scholar
- Scholl A, Becker C (2006) State-of-the-art exact and heuristic solution procedures for simple assembly line balancing. Eur J Oper Res 168:666–693CrossRefGoogle Scholar
- Simaria AS, Vilarinho PM (2009) 2-ANTBAL: an ant colony optimisation algorithm for balancing two-sided assembly lines. Comput Ind Eng 56:489–506CrossRefGoogle Scholar
- Sivasankaran P, Shahabudeen P (2014) Literature review of assembly line balancing problems. Int J Adv Manuf Technol. doi: 10.1007/s00170-014-5944-y Google Scholar
- Taha RB, El-Kharbotly AK, Sadek YM, Afia NH (2011) A genetic algorithm for solving two-sided assembly line balancing problems. Ain Shams Eng J 2:227–240CrossRefGoogle Scholar
- Tapkan P, Özbakir L, Baykasoğlu A (2012) Modeling and solving constrained two-sided assembly line balancing problem via bee algorithms. Appl Soft Comput J 12(11):3343–3355CrossRefGoogle Scholar
- Tapkan P, Özbakir L, Baykasoglu A (2012) Bees algorithm for constrained fuzzy multi-objective two-sided assembly line balancing problem. Optim Lett 6(6):1039–1049CrossRefGoogle Scholar
- Wang B, Guan Z, Li D, Zhang C, Chen L (2014) Two-sided assembly line balancing with operator number and task constraints: a hybrid imperialist competitive algorithm. Int J Adv Manuf Technol. doi: 10.1007/s00170-014-5816-5 Google Scholar
- Wu E-F, Jin Y, Bao J-S, Hu X-F (2008) A branch-and-bound algorithm for two-sided assembly line balancing. Int J Adv Manuf Technol 39:1009–1015CrossRefGoogle Scholar
- Xiaofeng H, Erfei W, Jinsong B, Ye J (2010) A branch-and-bound algorithm to minimize the line length of a two-sided assembly line. Eur J Oper Res 206(3):703–707CrossRefGoogle Scholar
- Yegul MF, Ağpak K, Yavuz M (2010) A new algorithm for U-shaped two-sided assembly line balancing. Trans Can Soc Mech Eng 34(2):225–241Google Scholar
- Yuan B, Zhang C, Shao X (2013) A late acceptance hill-climbing algorithm for balancing two-sided assembly lines with multiple constraints. J Intell Manuf. doi: 10.1007/s10845-013-0770-x Google Scholar