Balancing Assembly Line with Moving Workers and Worker-Dependent Task Times Using Linear Programming Formulation

Year 2026, Volume: 15 Issue: 1 , 177 - 187 , 24.03.2026

Murat Sahin , İsmet Soylemez

https://doi.org/10.17798/bitlisfen.1785785

https://izlik.org/JA85HL53PD

Abstract

This study addresses the moving heterogeneous worker assembly line balancing problem, a new variant of the classical problem that simultaneously considers worker-dependent task times and worker mobility between stations. In this setting, the processing time of each task differs according to the skills and efficiency of the assigned worker, while workers are allowed to move within a limited range to perform tasks at different stations. These features make the problem more realistic but also substantially more complex, as precedence relations, heterogeneous workloads, cycle time restrictions, and worker movements must all be satisfied simultaneously. To capture these interrelated aspects, mixed integer linear programming is proposed, which can provide exact solutions for small-sized instances. A dataset based on well-known precedence diagrams is generated to evaluate model performance across varying levels of task time variability and worker–station configurations.
The results show that the formulation optimally solves small-sized instances, whereas medium and large instances remain computationally demanding, with increasing gaps and longer solving times. The findings further reveal that adding an extra workstation can improve efficiency, especially in larger-sized problem instances. Overall, this study contributes to assembly line literature with a novel mathematical model that integrates worker heterogeneity and mobility, highlighting future research opportunities for heuristic and metaheuristic approaches.

Keywords

Assembly line balancing problem , Mixed integer linear programming , Walking workers , Worker dependent task times , Workforce heterogeneity.

Ethical Statement

There is no conflict of interest between the authors. The study is complied with research and publication ethics.

References

• A. Yoosefelahi, M. Aminnayeri, H. Mosadegh, and H. D. Ardakani. Type II robotic assembly line balancing problem: An evolution strategies algorithm for a multi-objective model. Journal of Manufacturing Systems, 31(2), 2012, 139-151.
• Y. Delice, E. K. Aydoğan, İ. Söylemez, and U. Özcan. An ant colony optimisation algorithm for balancing two-sided U-type assembly lines with sequence-dependent set-up times. Sādhanā, 43(12), 2018, 199.
• M. C. O. Moreira, J. F. Cordeau, A. M. Costa, and G. Laporte. Robust assembly line balancing with heterogeneous workers. Computers and Industrial Engineering, 88, 2015, 254-263.
• N. P. B. Campana, M. Iori, and M. C. O. Moreira. Mathematical models and heuristic methods for the assembly line balancing problem with hierarchical worker assignment. International Journal of Production Research, 60(7), 2022, 2193-2211.
• B. Sungur, and Y. Yavuz. Assembly line balancing with hierarchical worker assignment. Journal of Manufacturing Systems, 37, 2015, 290-298.
• O. Polat, C. B. Kalayci, Ö. Mutlu and S. M. Gupta. A two-phase variable neighbourhood search algorithm for assembly line worker assignment and balancing problem type-II: an industrial case study. International Journal of Production Research, 54(3), 2016, 722-741.
• Q. Wang, G. W. Owen, and A. R. Mileham. Determining numbers of workstations and operators for a linear walking-worker assembly line. International Journal of Computer Integrated Manufacturing, 20(1), 2007, 1-10.
• C. G. S. Sikora, T. C. Lopes, and L. Magatão. Traveling worker assembly line (re) balancing problem: Model, reduction techniques, and real case studies. European Journal of Operational Research, 259(3), 2017, 949-971.
• M. Şahin, and T. Kellegöz. Balancing multi-manned assembly lines with walking workers: problem definition, mathematical formulation, and an electromagnetic field optimization algorithm. International Journal of Production Research, 57(20), 2019, 6487-6505.
• M. Liu, Z. Liu, F. Chu, R. Liu, F. Zheng, and C. Chu. Risk-averse assembly line worker assignment and balancing problem with limited temporary workers and moving workers. International Journal of Production Research, 60(23), 2022, 7074-7092.
• S. Lassalle, Q. Wang, G. W. Owen, and A. R. Mileham. A study of in-process waiting time on a linear walking worker assembly line. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 221(12), 2007, 1763-1770.
• J. P. Shewchuk. Worker allocation in lean U-shaped production lines. International Journal of Production Research, 46(13), 2008, 3485-3502.
• R. Sirovetnukul and P. Chutima. The impact of walking time on U-shaped assembly line worker allocation problems. Engineering Journal, 14(2), 2010, 53.
• A. Al-Zuheri, L. Luong, and K. Xing. The role of randomness of a manual assembly line with walking workers on model validation. Procedia CIRP, 3, 2012, 233-238.
• E. Cevikcan. A mathematical programming approach for walking-worker assembly systems. Assembly Automation, 34(1), 2014, 56-68.
• A. Al-Zuheri, L. Luong, and K. Xing. A framework supporting the design of walking worker assembly line towards improving productivity and ergonomics performance, Int. Journal of Engineering Research and Application 4(3), 2014, 514-523.
• A. Deepak, R. Srivatsan, and V. Samsingh. A case study on implementation of walking worker assembly line to improve productivity and utilisation of resources in a heavy duty manufacturing industry. FME Transactions, 45(4), 2017, 497.
• S. E. H. Petroodi, S. Thevenin, S. Kovalev, and A. Dolgui. Markov decision process for multi-manned mixed-model assembly lines with walking workers. International Journal of Production Economics, 255, 2023, 108661.
• M. K. Oksuz, K. Buyukozkan, and S. I. Satoglu. U-shaped assembly line worker assignment and balancing problem: A mathematical model and two meta-heuristics. Computers and Industrial Engineering, 112, 2017, 246-263.
• Z. Zhang, Q. Tang, D. Han, and Z. Li. Enhanced migrating birds optimization algorithm for U-shaped assembly line balancing problems with workers assignment. Neural Computing and Applications, 31, 2019, 7501-7515.
• M. N. Janardhanan, Z. Li, and P. Nielsen. Model and migrating birds optimization algorithm for two-sided assembly line worker assignment and balancing problem. Soft Computing, 23, 2019, 11263-11276.
• C. Miralles, J. B. Garcia-Sabater, C. Andres, and M. Cardos. Branch and bound procedures for solving the Assembly Line Worker Assignment and Balancing Problem: Application to Sheltered Work Centres for Disabled. Discrete Applied Mathematics, 156(3), 2008, 352–367.
• C. Blum, and C. Miralles. On solving the assembly line worker assignment and balancing problem via beam search. Computers and Operations Research, 38(1), 2011, 328-339.
• F. F. Araujo, A. M. Costa, and C. Miralles. Two extensions for the ALWABP: Parallel stations and collaborative approach. International Journal of Production Economics, 140(1), 2012, 483-495.
• L. Borba and M. Ritt. A heuristic and a branch-and-bound algorithm for the assembly line worker assignment and balancing problem. Computers and Operations Research, 45, 2014, 87-96.
• R. Ramezanian and A. Ezzatpanah. Modeling and solving multi-objective mixed-model assembly line balancing and worker assignment problem. Computers and Industrial Engineering, 87, 2015, 74-80.
• M. C. O. Moreira, R. Pastor, A. M. Costa and C. Miralles. The multi-objective assembly line worker integration and balancing problem of type-2. Computers and Operations Research, 82, 2017, 114-125.
• S. D. Akyol and A. Baykasoğlu. ErgoALWABP: A multiple-rule based constructive randomized search algorithm for solving assembly line worker assignment and balancing problem under ergonomic risk factors. Journal of Intelligent Manufacturing, 30, 2019, 291-302.
• A. Karas and F. Ozcelik. Assembly line worker assignment and rebalancing problem: A mathematical model and an artificial bee colony algorithm. Computers and Industrial Engineering, 156, 2021, 107195.
• A. S. Michels and A. M. Costa. Model and heuristics for the multi-manned assembly line worker integration and balancing problem, International Journal of Production Research, 62(24), 2024, 8719-8744.