Skip to main content
Log in

Local search methods for type I mixed-model two-sided assembly line balancing problems

  • Regular Research Paper
  • Published:
Memetic Computing Aims and scope Submit manuscript

Abstract

Two-sided assembly lines are widely utilized to assemble large-sized products such as cars and trucks. Recently, these types of assembly lines have been applied to assemble different types of products due to a large variety of customer demands and strong market competition. This paper presents two simple local search methods, the iterated greedy algorithm and iterated local search algorithm, to deal with type I mixed-model two-sided assembly line balancing problems. These two algorithms utilize new precedence-based local search functions with referenced permutation and two neighborhood structures to emphasize intensification while preserving high search speed. Additionally, these local search methods are enhanced by utilizing the best decoding scheme amongst nine candidates and a new station-oriented evaluation to guide the search direction. New lower bound calculations are also presented to check the optimality of the achieved solutions. Eleven recent and high-performing metaheuristic algorithms are re-implemented to test the performance of the proposed algorithms. A comprehensive study on a set of benchmark problems demonstrates the advantages of the improvements and the superiority of the two proposed methods. Experimental results show that the proposed algorithms obtain 23 new upper bounds compared with two recently published algorithms, among which 19 cases are proven to be optimal for the first time.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. 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 74:1005–1016

    Article  Google Scholar 

  2. Bartholdi J (1993) Balancing two-sided assembly lines: a case study. Int J Prod Res 31:2447–2461

    Article  Google Scholar 

  3. Battaïa O, Dolgui A (2013) A taxonomy of line balancing problems and their solution approaches. Int J Prod Econ 142:259–277

    Article  Google Scholar 

  4. Baykasoglu A, Dereli T (2008) Two-sided assembly line balancing using an ant-colony-based heuristic. Int J Adv Manuf Technol 36:582–588. https://doi.org/10.1007/s00170-006-0861-3

    Article  Google Scholar 

  5. Delice Y, Kızılkaya Aydoğan E, Özcan U, İlkay MS (2017) A modified particle swarm optimization algorithm to mixed-model two-sided assembly line balancing. J Intell Manuf 28:23–36. https://doi.org/10.1007/s10845-014-0959-7

    Article  MATH  Google Scholar 

  6. Hu X, Wu E, Jin Y (2008) A station-oriented enumerative algorithm for two-sided assembly line balancing. Eur J Oper Res 186:435–440. https://doi.org/10.1016/j.ejor.2007.01.022

    Article  MATH  Google Scholar 

  7. Khorasanian D, Hejazi SR, Moslehi G (2013) Two-sided assembly line balancing considering the relationships between tasks. Comput Ind Eng 66:1096–1105. https://doi.org/10.1016/j.cie.2013.08.006

    Article  Google Scholar 

  8. Kim YK, Kim Y, Kim YJ (2000) Two-sided assembly line balancing: a genetic algorithm approach. Prod. Plan. Control 11:44–53. https://doi.org/10.1080/095372800232478

    Article  Google Scholar 

  9. Kim YK, Song WS, Kim JH (2009) A mathematical model and a genetic algorithm for two-sided assembly line balancing. Comput Oper Res 36:853–865. https://doi.org/10.1016/j.cor.2007.11.003

    Article  MATH  Google Scholar 

  10. Kucukkoc I, Li Z, Karaoglan AD, Zhang DZ (2018) Balancing of mixed-model two-sided assembly lines with underground workstations: a mathematical model and ant colony optimization algorithm. Int J Prod Econ 205:228–243. https://doi.org/10.1016/j.ijpe.2018.08.009

    Article  Google Scholar 

  11. Kucukkoc I, Zhang DZ (2014) Mathematical model and agent based solution approach for the simultaneous balancing and sequencing of mixed-model parallel two-sided assembly lines. Int J Prod Econ 158:314–333. https://doi.org/10.1016/j.ijpe.2014.08.010

    Article  Google Scholar 

  12. Kucukkoc I, Zhang DZ (2016) Mixed-model parallel two-sided assembly line balancing problem: a flexible agent-based ant colony optimization approach. Comput Ind Eng 97:58–72. https://doi.org/10.1016/j.cie.2016.04.001

    Article  Google Scholar 

  13. Lee TO, Kim Y, Kim YK (2001) Two-sided assembly line balancing to maximize work relatedness and slackness. Comput Ind Eng 40:273–292. https://doi.org/10.1016/S0360-8352(01)00029-8

    Article  Google Scholar 

  14. Li D, Zhang C, Tian G, Shao X, Li Z (2018) Multiobjective program and hybrid imperialist competitive algorithm for the mixed-model two-sided assembly lines subject to multiple constraints. IEEE Trans. Syst. Man Cybern. Syst. 48:119–129. https://doi.org/10.1109/TSMC.2016.2598685

    Article  Google Scholar 

  15. Li Z, Kucukkoc I, Nilakantan JM (2017) Comprehensive review and evaluation of heuristics and meta-heuristics for two-sided assembly line balancing problem. Comput Oper Res 84:146–161. https://doi.org/10.1016/j.cor.2017.03.002

    Article  MathSciNet  MATH  Google Scholar 

  16. Li Z, Tang Q, Zhang L (2016) Minimizing the cycle time in two-sided assembly lines with assignment restrictions: improvements and a simple algorithm. Math. Probl. Eng. 2016:1–15. https://doi.org/10.1155/2016/4536426

    Article  MathSciNet  MATH  Google Scholar 

  17. Li Z, Tang Q, Zhang L (2017) Two-sided assembly line balancing problem of type I: improvements, a simple algorithm and a comprehensive study. Comput Oper Res 79:78–93. https://doi.org/10.1016/j.cor.2016.10.006

    Article  MathSciNet  MATH  Google Scholar 

  18. Özcan U, Toklu B (2009) Balancing of mixed-model two-sided assembly lines. Comput Ind Eng 57:217–227. https://doi.org/10.1016/j.cie.2008.11.012

    Article  MATH  Google Scholar 

  19. Özcan U, Toklu B (2009) A tabu search algorithm for two-sided assembly line balancing. Int J Adv Manuf Technol 43:822–829

    Article  Google Scholar 

  20. Özcan U, Toklu B (2010) Balancing two-sided assembly lines with sequence-dependent setup times. Int J Prod Res 48:5363–5383. https://doi.org/10.1080/00207540903140750

    Article  MATH  Google Scholar 

  21. Pan Q-K, Ruiz R (2012) Local search methods for the flowshop scheduling problem with flowtime minimization. Eur J Oper Res 222:31–43. https://doi.org/10.1016/j.ejor.2012.04.034

    Article  MathSciNet  MATH  Google Scholar 

  22. Purnomo HD, Wee H-M, Rau H (2013) Two-sided assembly lines balancing with assignment restrictions. Math Comput Model 57:189–199. https://doi.org/10.1016/j.mcm.2011.06.010

    Article  MATH  Google Scholar 

  23. Ruiz R, Stützle T (2007) A simple and effective iterated greedy algorithm for the permutation flowshop scheduling problem. Eur J Oper Res 177:2033–2049

    Article  Google Scholar 

  24. Simaria AS, Vilarinho PM (2009) 2-ANTBAL: an ant colony optimisation algorithm for balancing two-sided assembly lines. Comput Ind Eng 56:489–506

    Article  Google Scholar 

  25. Tang Q, Li Z, Zhang L (2016) An effective discrete artificial bee colony algorithm with idle time reduction techniques for two-sided assembly line balancing problem of type-II. Comput Ind Eng 97:146–156. https://doi.org/10.1016/j.cie.2016.05.004

    Article  Google Scholar 

  26. Yang W, Cheng W (2019) Modelling and solving mixed-model two-sided assembly line balancing problem with sequence-dependent setup time. J. Prod. Res, Int. https://doi.org/10.1080/00207543.2019.1683255

    Book  Google Scholar 

  27. Yuan B, Zhang C, Shao X, Jiang Z (2015) An effective hybrid honey bee mating optimization algorithm for balancing mixed-model two-sided assembly lines. Comput Oper Res 53:32–41. https://doi.org/10.1016/j.cor.2014.07.011

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

This project is partially supported by National Natural Science Foundation of China under Grants 51875421 and 61803287 and the China Postdoctoral Science Foundation under Grant 2018M642928. The authors are grateful for the insightful comments by the anonymous referees which helped to improve this paper.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mukund Nilakantan Janardhanan.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix A: Illustrated decoding procedure

Appendix A: Illustrated decoding procedure

1.1 Utilized notations for decoding procedure

\( i,h,p \)

The index of tasks

\( I \)

Set of tasks; \( i,h \in I \)

\( j \)

The index of mated-stations

\( J \)

Set of mated-stations; \( j \in J \)

\( k \)

The index of sides, \( k = 1,2 \)

\( m \)

The index of the product models

\( M \)

Set of product models; \( m \in M \)

\( A_{L} \)

Set of tasks that should be allocated to the left side of a mated-station

\( A_{R} \)

Set of tasks that should be allocated to the right side of a mated-station

\( A_{E} \)

Set of tasks that should be allocated to either side of a mated-station

\( P\left( h \right) \)

Set of immediate predecessors of task \( h \)

\( t_{h}^{m} \)

Operation time of task \( h \) for model \( m \)

\( tf_{h}^{m} \)

Completion time of task \( h \) for model \( m \)

\( wl_{j}^{m} \)

The completion time of the left-side workstation of the mated-station \( j \) (including the idle time) for model \( m \)

\( wr_{j}^{m} \)

The completion time of the right-side workstation of the mated-station \( j \) (including the idle time) for model \( m \)

\( SL_{j} \)

Set of tasks that have been allocated to the left side of mated-station \( j \)

\( SR_{j} \)

Set of tasks that have been allocated to the right side of mated-station \( j \)

\( ATL_{j} \)

Set of assignable tasks that can be allocated to the left side of mated-station \( j \)

\( ATR_{j} \)

Set of assignable tasks that can be allocated to the right side of mated-station \( j \)

\( CT \)

Cycle time

\( Nt \)

Total number of tasks

\( nm,nl,nr \)

The number of mated-stations, left-side workstation, and right-side workstations

\( ns \)

The total number of workstations

The decoding procedure of TSD4 is detailed as follows, and serves as an example.

figure b

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, Z., Janardhanan, M.N., Tang, Q. et al. Local search methods for type I mixed-model two-sided assembly line balancing problems. Memetic Comp. 13, 111–130 (2021). https://doi.org/10.1007/s12293-020-00319-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12293-020-00319-0

Keywords

Navigation