An iterative decomposition for asynchronous mixed-model assembly lines: combining balancing, sequencing, and buffer allocation

Asynchronous Mixed-Model Assembly lines are common production layouts dedicated to large-scale manufacturing of similar products. Cyclically scheduling such products is an interesting strategy to obtain high and stable throughput. In order to best optimise these lines, it is necessary to combine line balancing, model sequencing, and buffer allocation. However, few works integrate these three degrees of freedom, and evaluating steady-state performance as a consequence of these decisions is challenging. This paper presents a mathematical model that allows an exact steady-state performance evaluation of these lines, and hence their optimisation. While the combination of degrees of freedom is advantageous, it is also computational costly. An iterative decomposition procedure based on alternation between two mathematical models and on optimality cuts is also presented. The decomposition is tested against the proposed mathematical model in a 700-instance dataset. The developed methods obtained 142 optimal answers. Results show that the decomposition outperforms the monolithic mathematical model, in particular for larger and harder instances in terms of solution quality. The optimality cuts are also shown to help the decomposition steps in terms of solution quality and time. Comparisons to a sequential procedure further demonstrate the importance of simultaneously optimising the three degrees of freedom, as both the proposed model and the decomposition outperformed such procedure.