Robust optimization for the integrated worker-cell assignment and sequencing problem in a lean U-shaped assembly line

Worker-cell allocation and sequencing problems play a central role in the optimization of mixed-model U-shaped assembly lines. Since this production layout is related to worker performance, we should consider the different skills of workers and their impact on actual working times and the resulting uncertainty. Thus, this research contributes to assigning workforce and determining model sequences in a lean U-shaped line, while workers are heterogonous and task processing times are uncertain. In order to overcome the uncertainty, an efficient robust optimization model is exerted. This study simultaneously focuses on integrating worker-cell assignment and sequencing models, due to the increasing importance of which. To do this, a non-linear programming (NLP) model is formulated. The proposed model is corroborated in small and medium scales using a commercial solver. Then, the Lagrangian relaxation (LR) algorithm is used for large-scale instances, so that bounds with tiny gaps within a reasonable interval are ensured. According to the results, the LR algorithm outperforms the commercial solver without LR in large-scale instances. The result shows that considering the sequencing concept leads to an improvement of the optimal value by two fifths. Moreover, not only does the LR algorithm solve large instances in logical CPU time, but also it shows only one in twenty deviations from the exact solutions.