, 43:199 | Cite as

An ant colony optimisation algorithm for balancing two-sided U-type assembly lines with sequence-dependent set-up times



Some practical arrangements in assembly lines necessitate set-up times between consecutive tasks. To create more realistic models of operations, set-up times must be considered. In this study, a sequence-dependent set-up times approach for two-sided u-type assembly line (TUAL) structures is proposed for the first time. Previous studies on TUAL have not included set-up times in their analyses. Furthermore, an algorithm based on the Ant Colony Optimization (ACO) algorithm, which is using a heuristic priority rule based procedure has been proposed in order to solve this new approach. In this paper, we look at the sequence-dependent set-up times between consecutive tasks and consecutive cycles, called the “forward set-up time” and the “backward set-up time”, respectively. Additionally, we examine the “crossover set-up time”, which arises from a new sequence of tasks in a crossover station. In order to model more realistic assembly line configurations, it is necessary to include sequence-dependent set-up times when computing all of the operational times such as task starting times and finishing times as well as the total workstation time. In this study, the proposed approach aims to minimize the number of mated-stations as the primary objective and to minimize the number of total workstations as a secondary objective. In order to evaluate the efficiency of the proposed algorithm, a computational study is performed. As can be seen from the experimental results the proposed approach finds promising results for all literature-test problems.


Assembly line balancing U-type assembly lines two-sided assembly lines sequence-dependent set-up times ant colony optimization priority rules 



Iteration size (number of iterations)


Iteration index \( \left( {1 \le iter \le IS} \right) \)


Colony size


Colony index \( \left( {1 \le a \le CS} \right) \)


Number of tasks


Task index \( \left( {1 \le i,j \le n} \right) \)


A list composed of candidate tasks

\( PM_{i,j} \)

Precedence matrix which keeps the precedence relations between all tasks

\( TM_{i,m } \)

Task matrix which keeps the required values of each task

\( \tau_{t,i} \)

Pheromone matrix saves real numbers which indicate the pheromone trail intensity of the task i stored in the tth task assignment process

\( \eta_{a,t} \)

Heuristic information matrix saves one of the six different heuristic information which is required to calculate the selection probability (P) of tth task assignment process for the ant a

\( S_{a,i,k} \)

Solution matrix saves detailed solutions for each task (i) of each ant

\( SR_{a,l} \)

Solution Result matrix saves objective function values for each ant


Position index


Station index


Assignment locations, (loc = 1,2, 3, 4)


The selected position for assignment, (pos = 1, 2, …, posmax)


Cycle time

\( t_{i} \)

Task time of each task, \( i \in \left\{ {1,2, \ldots ,n} \right\} \)

\( fs_{i,j} \)

Forward set-up time for all \( i,j \in \left\{ {1,2, \ldots ,n} \right\} \)

\( bs_{i,j} \)

Backward set-up time for all \( i,j \in \left\{ {1,2, \ldots ,n} \right\} \)

\( cs_{i,j} \)

Crossover set-up time for all \( i,j \in \left\{ {1,2, \ldots ,n} \right\} \)

\( FSM_{i,j} \)

Forward set-up matrix consists of the setup values between each task, for all \( i,j \;\;{\text{where}}\; i,j \in \left\{ {1,2, \ldots ,n} \right\} \)

\( BSM_{i,j} \)

Backward set-up matrix consists of the setup values between each task, for all \( i,j \;\;{\text{where}}\; i,j \in \left\{ {1,2, \ldots ,n} \right\} \)

\( CSM_{i,j} \)

Crossover set-up matrix consists of the setup values between each task, for all \( i,j \;\;{\text{where}}\; i,j \in \left\{ {1,2, \ldots ,n} \right\} \)

\( {\text{F}}_{pos,loc} \)

The feasibility value of the current assignment operation at position pos and location loc

\( RT_{pos,loc} \)

Remainder time of the current assignment operation at position pos and location loc

\( X_{r,i} \)

It is used to save all of the priority rule values, which are determined in the initialization step, for all tasks i in CL

\( pr_{i} \)

It is used to save all of the calculated relative priority rule value of each candidate task

\( P_{i} \)

The selection probability value of task i. It is calculated using the ant’s pheromone value and the selected priority rule

\( SP_{l} \)

Cumulative selection probability matrix



This research was supported by Scientific Research Fund of Erciyes University under the contract no: FBA-2017-7349.


  1. 1.
    Boysen N, Fliedner M and Scholl A 2007 A classification of assembly line balancing problems. Eur. J. Oper. Res. 183: 674–693zbMATHCrossRefGoogle Scholar
  2. 2.
    Li M, Tang Q, Zheng Q, Xia X and Floudas C A 2017 A Rules-based heuristic approach for the U-shaped assembly line balancing problem. Appl. Math. Modell. MathSciNetCrossRefGoogle Scholar
  3. 3.
    Becker C and Scholl A 2006 A survey on problems and methods in generalized assembly line balancing. Eur. J. Oper. Res. 168: 694–715MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Salveson M E 1955 The assembly line balancing problem. J. Ind. Eng. 6(6): 18–25MathSciNetGoogle Scholar
  5. 5.
    Urban T L and Chiang W C 2006 An optimal piecewise-linear program for the U-line balancing problem with stochastic task times. Eur. J. Oper. Res. 168(3): 771–782MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Boysen N, Fliedner M and Scholl A 2008 Assembly line balancing: Which model to use when? Int. J. Product. Econ. 111: 509–528zbMATHCrossRefGoogle Scholar
  7. 7.
    Battaia O and Dolgu A 2013 A taxonomy of line balancing problems and their solution approaches. Int. J. Product. Econ. 142: 259–277CrossRefGoogle Scholar
  8. 8.
    Sivasankaran P and Shahabudeen P 2014 Literature review of assembly line balancing problems. Int. J. Adv. Manuf. Technol. 73: 1665–1694CrossRefGoogle Scholar
  9. 9.
    Kim Y K, Kim Y, Kim Y J 2000 Two-sided assembly line balancing: a genetic algorithm approach. Product. Plan. Control 11: 44–53CrossRefGoogle Scholar
  10. 10.
    Bartholdi J J 1993 Balancing two-sided assembly lines: A case study. Int. J. Product. Res. 31: 2447–2461CrossRefGoogle Scholar
  11. 11.
    Lee T O, Kim Y and Kim Y K 2001 Two-sided assembly line balancing to maximize work relatedness and slackness. Comput. Ind. Eng. 40: 273–292CrossRefGoogle Scholar
  12. 12.
    Miltenburg J and Wijngaard J 1994 The U-line balancing problem. Manag. Sci. 40(10): 1378–1388zbMATHCrossRefGoogle Scholar
  13. 13.
    Urban T L 1998 Optimal balancing of U-shaped assembly lines. Manag. Sci. 44(5): 738–741zbMATHCrossRefGoogle Scholar
  14. 14.
    Aigbedo H and Monden Y 1997 A parametric procedure for multi-criterion sequence scheduling for just-in-time mixed-model assembly lines. Int. J. Product. Res. 35: 2543–2564zbMATHCrossRefGoogle Scholar
  15. 15.
    Miltenburg J 1998 Balancing U-lines in a multiple U-line facility. Eur. J. Oper. Res. 109: 1–23zbMATHCrossRefGoogle Scholar
  16. 16.
    Yegül M F, Ağpak K and Yavuz M 2010 A new algorithm for U-shaped two-sided assembly line balancing. Trans. Can. Soc. Mech. Eng. 34(2): 225–241CrossRefGoogle Scholar
  17. 17.
    Ağpak K, Yegül M F and Gökçen, H 2012 Two-sided U-type assembly line balancing problem. Int. J. Product. Res. 50(18): 5035–5047CrossRefGoogle Scholar
  18. 18.
    Delice Y, Aydoğan E K, Özcan and İlkay M S 2017 Balancing two-sided U-type assembly lines using modified particle swarm optimization algorithm. 4OR 15: 37–66Google Scholar
  19. 19.
    Delice Y, Kızılkaya Aydoğan E and Özcan U 2016 Stochastic two-sided U-type assembly line balancing: a genetic algorithm approach. Int. J. Product. Res. 54(11): 3429–3451CrossRefGoogle Scholar
  20. 20.
    Andrés C, Miralles C and Pastor R 2008 Balancing and scheduling tasks in assembly lines with sequence-dependent setup times. Eur. J. Oper. Res. 187(3): 1212–1223zbMATHCrossRefGoogle Scholar
  21. 21.
    Scholl A, Boysen N and Fliedner M 2008 The sequence-dependent assembly line balancing problem. OR Spectr. 30(3): 579–609MathSciNetzbMATHCrossRefGoogle Scholar
  22. 22.
    Martino L and Pastor R 2010 Heuristic procedures for solving the general assembly line balancing problem with setups. Int. J. Product. Res. 48(6): 1787–1804CrossRefGoogle Scholar
  23. 23.
    Özcan U and Toklu B 2010 Balancing two-sided assembly lines with sequence-dependent setup times. Int. J. Product. Res. 48(18): 5363–5383zbMATHCrossRefGoogle Scholar
  24. 24.
    Nazarian E, Ko J and Wang H 2010 Design of multi-product manufacturing lines with the consideration of product change dependent inter-task times, reduced changeover and machine flexibility. J. Manuf. Syst. 29(1): 35–46CrossRefGoogle Scholar
  25. 25.
    Seyed-Alagheband S A, Ghomi S F and Zandieh M 2011 A simulated annealing algorithm for balancing the assembly line type II problem with sequence-dependent setup times between tasks. Int. J. Product. Res. 49(3): 805–825CrossRefGoogle Scholar
  26. 26.
    Yolmeh A and Kianfar F 2012 An efficient hybrid genetic algorithm to solve assembly line balancing problem with sequence-dependent setup times. Comput. Ind. Eng. 62(4): 936–945CrossRefGoogle Scholar
  27. 27.
    Hamta N, Ghomi S F, Jolai F and 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. Int. J. Product. Econ. 141(1): 99–111CrossRefGoogle Scholar
  28. 28.
    Akpinar Ş, Bayhan G M and Baykasoğlu A 2013 Hybridizing ant colony optimization via genetic algorithm for mixed-model assembly line balancing problem with sequence dependent setup times between tasks. Appl. Soft Comput. 13(1): 574–589CrossRefGoogle Scholar
  29. 29.
    Scholl A, Boysen N and Fliedner M 2013 The assembly line balancing and scheduling problem with sequence-dependent setup times: problem extension, model formulation and efficient heuristics. OR Spectr. 35(1): 291–320MathSciNetzbMATHCrossRefGoogle Scholar
  30. 30.
    Akpinar Ş and Baykasoğlu A 2014 Modeling and solving mixed-model assembly line balancing problem with setups. Part I: A mixed integer linear programming model. J. Manuf. Syst. 33(1): 177–187CrossRefGoogle Scholar
  31. 31.
    Akpinar Ş and Baykasoğlu A 2014 Modeling and solving mixed-model assembly line balancing problem with setups. Part II: A multiple colony hybrid bees algorithm. J. Manuf. Syst. 33(4): 445–461CrossRefGoogle Scholar
  32. 32.
    Esmaeilbeigi R, Naderi B and Charkhgard P 2016 New formulations for the setup assembly line balancing and scheduling problem. OR Spectr. 38: 493–518MathSciNetzbMATHCrossRefGoogle Scholar
  33. 33.
    Şahin M and Kellegöz T 2017 Increasing production rate in U-type assembly lines with sequence-dependent set-up times. Eng. Optim. 49(8): 1401–1419MathSciNetCrossRefGoogle Scholar
  34. 34.
    Akpinar Ş, Elmi A and Bektaş T 2017 Combinatorial Benders cuts for assembly line balancing problems with setups. Eur. J. Oper. Res. 259(2): 527–537MathSciNetzbMATHCrossRefGoogle Scholar
  35. 35.
    Gutjahr A L and Nemhauser G L 1964 An algorithm for the line balancing problem. Manag. Sci. 11(2): 308–315MathSciNetzbMATHCrossRefGoogle Scholar
  36. 36.
    Mogale D G, Kumar M, Kumar S K and Tiwari M K 2018 Grain silo location-allocation problem with dwell time for optimization of food grain supply chain network. Transp. Res. Part E 111: 40–69CrossRefGoogle Scholar
  37. 37.
    Mogale D G, Kumar S K and Tiware M K 2018 An MINLP model to support the movement and storage decisions of the Indian food grain supply chain. Control Eng. Pract. 70: 98–113CrossRefGoogle Scholar
  38. 38.
    Blum C 2005 Beam-ACO - Hybridizing ant colony optimization with beam search: An application to open shop scheduling. Comput. Oper. Res. 32(6): 1565–1591zbMATHCrossRefGoogle Scholar
  39. 39.
    Ding Q, Hu X, Sun L and Wang Y 2012 An improved ant colony optimization and its application to vehicle routing problem with time windows. Neurocomputing 98: 101–107CrossRefGoogle Scholar
  40. 40.
    Mogale D G, Dolgui A, Kandhway R, Kumar S K and Tiwari M K 2017 A multi-period inventory transportation model for tactical planning of food grain supply chain. Comput. Ind. Eng. 110: 379–394CrossRefGoogle Scholar
  41. 41.
    Dorigo M and Stützle T 2009 Ant colony optimization: Overview and recent advances. Techreport, IRIDIA. Universite Libre de BruxelleszbMATHGoogle Scholar
  42. 42.
    Colorni A, Dorigo M and Maniezzo V 1991 Distributed optimization by ant colonies. In: Proceedings of ECAL 91-European Conference on Artificial Life, Paris, France. Elsevier, Amsterdam, pp. 134–142Google Scholar
  43. 43.
    Colorni A, Dorigo M and Maniezzo V 1992 An investigation of some properties of an ant algorithm. In: Manner R, Manderick B (Eds.), In: Proceedings of the Parallel Problem Solving from Nature Conference (PPSN 92), Brussels, Belgium. Elsevier, Amsterdam, pp. 509–520Google Scholar
  44. 44.
    Bautista J and Pereira J 2002 Ant algorithms for assembly line balancing. In: Lecture Notes in Computer Science 2463: 65–75CrossRefGoogle Scholar
  45. 45.
    Bautista J and Pereira J 2007 Ant algorithms for a time and space constrained assembly line balancing problem. Eur. J. Oper. Res. 177: 2016–2032zbMATHCrossRefGoogle Scholar
  46. 46.
    McMullen P R and Tarasewich P 2003 Using ant techniques to solve the assembly line balancing problem. IIE Trans. 35: 605–617CrossRefGoogle Scholar
  47. 47.
    Sabuncuoglu I, Erel E and Alp A 2009 Ant colony optimization for the single model U-type assembly line balancing problem. Int. J. Product. Econ. 120: 287–300CrossRefGoogle Scholar
  48. 48.
    Simaria A S and Vilarinho P M 2009 2-ANTBAL: An ant colony optimisation algorithm for balancing two-sided assembly lines. Comput. Ind. Eng. 56, 489–506CrossRefGoogle Scholar
  49. 49.
    Yagmahan B 2011 Mixed-model assembly line balancing using a multi-objective ant colony optimization approach. Expert Syst. Appl. 38: 12453–12461CrossRefGoogle Scholar
  50. 50.
    Kucukkoc I and Zhang D Z 2016 Mixed-model parallel two-sided assembly line balancing problem: a flexible agent-based ant colony optimization approach. Comput. Ind. Eng. 97: 58–72CrossRefGoogle Scholar
  51. 51.
    Bautista J, Suarez R, Mateo M and Companys R 2000 Local search heuristics for the assembly line balancing problem with incompatibilities between tasks. In: Proceedings of the IEEE international conference on robotics and automation. San Francisco, CA, pp. 2404–2409Google Scholar
  52. 52.
    Helgeson W and Birnie D 1961 Assembly line balancing using the ranked positional weight technique. J. Ind. Eng. 12: 394–398Google Scholar
  53. 53.
    Tonge F 1961 A Heuristic Program of Assembly Line Balancing. Englewood Cliffs, NJ: Prentice-HallGoogle Scholar
  54. 54.
    Kilbridge M and Wester L 1961 A heuristic method for assembly line balancing. J. Ind. Eng. 12: 292–298Google Scholar
  55. 55.
    Arcus A L 1963 An analysis of a computer method of sequencing assembly line operations. PhD dissertation. University of California, BerkeleyGoogle Scholar
  56. 56.
    Moodie C L and Young H H 1965 A heuristic method of assembly line balancing for assumptions of constant or variable work element times. J. Ind. Eng. 16: 23–29Google Scholar
  57. 57.
    Brian T F and Patterson J H 1984 An integer programming algorithm with network cuts for solving the assembly line balancing problem. Manag. Sci. 30(1): 85–99zbMATHCrossRefGoogle Scholar
  58. 58.
    Elsayed E A and Boucher T O 1994 Analysis and Control of Production Systems. New Jersey: Prentice Hall International Series in Industrial and Systems EngineeringGoogle Scholar
  59. 59.
    Talbot F B, Patterson J H and Gehrlein W V 1986 A comparative evaluation of heuristic line balancing techniques. Manag. Sci. 32(4): 430–454CrossRefGoogle Scholar
  60. 60.
    Scholl A and VoB S 1994 A note on fast, effective heuristics for simple assembly line balancing, Working paper, TH DarmstadtGoogle Scholar
  61. 61.
    Boctor F F 1995 A Multiple-rule heuristic for assembly line balancing. J. Oper. Res. Soc. 46: 62–69zbMATHCrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 2018

Authors and Affiliations

    • 1
    • 2
    • 3
    • 4
    • 4
  1. 1.Department of Management and Organization, Develi Vocational CollegeErciyes UniversityDeveli, KayseriTurkey
  2. 2.Department of Industrial EngineeringErciyes UniversityTalas, KayseriTurkey
  3. 3.Department of Industrial EngineeringAbdullah Gül UniversityKocasinan, KayseriTurkey
  4. 4.Department of Industrial EngineeringGazi UniversityMaltepe, AnkaraTurkey

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