An Optimization Approach for Solving a Mixed Model Assembly Line Balancing Problem with Collaborative Robots (Cobots) by Considering Time-weighted Average (TWA) Ergonomic Risk Score
10.14416/j.ind.tech.2025.12.013
Keywords:
Mixed-model Assembly Line Balancing, Ergonomic Risk Assessment, Collaborative Robot, Aging Society, Branch and Cut Algorithm, LinearizationAbstract
The objective of this research is to develop a mathematical model of the Mixed-Model Assembly Line Balancing Problem Type II (MMALBP-II) with collaborative robots (Cobots) considering time-weighted average (TWA) ergonomic risk score, and to test the performance of solving the model using the Branch and Cut method to reduce ergonomic risk for both working-age and elderly workers through human–Cobot collaboration. The performance evaluation using IBM ILOG CPLEX 22.1.2 showed that the model could solve benchmark balancing problems and find feasible solutions in 63 out of 75 experiments (84%). Optimal solutions were found in 53 out of 75 experiments (70.6%). On average, the total %gap of the total cycle time deviated from the lower bound of the average cycle time by 17.9%. The results further indicated that Branch and Cut could solve small- and medium-sized problems within the time limit (3600 seconds), with an average optimality %gap of 0% and 4.8%, respectively. However, for large-sized problems, in 12 out of 15 cases, Branch and Cut was unable to find a feasible solution within the given time.
References
https://population.un.org (Access on 10 August 2025)
L. McAtamney and E. Nigel, RULA: A survey method for the investigation of work-related upper limb disorders, Applied Ergonomics, 1993, 24(2), 91-99.
C. Jaturanonda and S. Nanthavanij, Heuristic procedure for two-criterion assembly line balancing problem, Industrial Engineering and Management Systems, 2006, 5(2), 84-96.
C. Jaturanonda, S. Nanthavanij and S. Das, Heuristic procedure for the assembly line balancing problem with postural load smoothness, International Journal of Occupational Safety and Ergonomics, 2013, 19(4), 531-541.
ISO/TS 15066:2016 Robots and Robotic Devices — Collaborative Robots, 2016.
C. Weckenborg, K. Kieckhäfer, C. Müller, M. Grunewald and T. Spengler, Balancing of assembly lines with collaborative robots, Business Research, 2019, 1–40
G. Bruno and D. Antonelli, Dynamic task classification and assignment for the management of human-robot collaborative teams in workcells, The International Journal of Advanced Manufacturing, 2018, 98(9-12), 2415–2427
https://www.ibm.com/docs/en/cofz/12.10.0?top ic=concepts-branch-cut-in-cplex (Access on 10 August 2025)
K, Stecke and M. Mokhtarzadeh, Balancing collaborative human–robot assembly lines to optimise cycle time and ergonomic risk, International Journal of Production Research, 2022, 60(1), 25-47
C. Sikora and C. Weckenborg, Balancing of assembly lines with collaborative robots: comparing approaches of the Benders’ decomposition algorithm, International Journal of Production Research, 2023, 61(15), 5117-5133.
C. Weckenborg and T. Spengler, Assembly Line Balancing with Collaborative Robots under consideration of Ergonomics: a cost-oriented approach, IFAC-PapersOnLine, 2019, 52(13), 1860-1865.
M. Mokhtarzadeh, M. Rabbani and N. Manavizadeh, A novel two-stage framework for reducing ergonomic risks of a mixed-model parallel U-shaped assembly-line, Applied Mathematical Modelling, 2021, 93, 597-613.
L. Tiacci, Assigning rest times to workers in assembly lines with ergonomically hazardous tasks: An approach to defend companies' profitability, International Journal of Production Research, 2024, 62(4), 1239-1261.
O. Polat, Ö. Mutlu, and E. Özgormus, A mathematical model for assembly line balancing problem type 2 under ergonomic workload constraint, The Ergonomics Open Journal, 2018, 11(1), 1-10.
H. Daneshmandi, D. Kee, M. Kamalinia, M. Oliaei and H. Mohammadi, An ergonomic intervention to relieve musculoskeletal symptoms of assembly line workers at an electronic parts manufacturer in Iran, Work, 2018, 61(4), 515–521.
K. Bouillet, S. Lemonnier, F. Clanche and G. Gauchard, Does the introduction of a cobot change the productivity and posture of the operators in a collaborative task?, PloS One, 2023, 18(8), e0289787.
K. Tung, Y. Fukumura, N. Baker, J. Forrest and S. Roll, Identifying an optimal sampling method to estimate postural risk in a dynamic work task, Proceedings of the Human Factors and Ergonomics Society Annual Meeting, 63(1), 1028-1033.
A. Börsch-Supan and M. Weiss, Productivity and age: Evidence from work teams at the assembly line, The Journal of the Economics of Ageing, 2016, 7, 30-42.
G.P. McCormick, Computability of global solutions to factorable nonconvex programs: Part I — Convex underestimating problems. Mathematical Programming, 1976, 10, 147-175.
A. Quenehen, N. Klement, A. Abdeljaouad, L. Roucoules and O. Gibaru, Economic and ergonomic performance enhancement in assembly process through multiple collaboration modes between human and robot, International Journal of Production Research, 2022, 61(5), 1517-1531.
E. Stecke and M. Mokhtarzadeh, Balancing collaborative human–robot assembly lines to optimise cycle time and ergonomic risk, International Journal of Production Research, 2021, 60(1), 25-47.
P. Mertens, Fließbandabstimmung mit dem Verfahren der begrenzten enumeration nach Müller- Merbach, Ablauf- und Planungsforschung, 8, 429 - 433.
J. Jackson, A computing procedure for a line balancing problem, Management Science, 1956, 2(3), 261-271.
E. Bowman, Assembly-line balancing by linear programming, Operations Research, 1967, 8(3), 385-389.
N. Thomopoulos, Line Balancing-Sequencing for mixed-model assembly, Management Science, 1967, 14(2), 59-75.
G. Buxey, Assembly line balancing with multiple stations, Management Science, 1974, 20(6), 1010-1021.
M. Kilbridge and L. Wester, A review of analytical systems of line balancing, Operations Research, 1962, 10(5), 626 - 638.
R. Hahn, Produktionsplanung bei Linienfertigung, De Gruyter, Berlin, Germany, 1972.
