Abstract
Asynchronous assembly lines are productive layouts in which products move sequentially between stations when processing at current station is complete, and the following station is empty. When these conditions are not verified, downstream starvations and upstream blockages can occur. Buffers are often employed to minimize these problems, which are particularly relevant when the line is shared between a set of different products models (mixed-model lines). If the sequence of such models is cyclical, a steady-state production rate is eventually reached. However, determining (and, therefore, optimizing) such steady-state is challenging. This led to the development of indirect performance measures for mixed-model lines by many authors. In this paper, a direct performance measure is presented with a mixed-integer linear programming model and compared to previous formulations. The model is also applied to a practical case study and to a new dataset (with 1050 instances), allowing general assertions on the problem. All instances are solved with a universal solver and solutions are validated with a simulation software. Tests on the dataset instances confirmed the observations made on the case study: the proposed formulation produced solutions with higher production rate in 82% of the instances and tied the remaining ones, not being outperformed a single time. A triple interdependency of task balancing, product sequencing, and buffer allocation is demonstrated. Cyclical schedules show how buffers are able to compensate differences between models across stations and lead to the conclusion that the propagation of differences of models between stations can generate scheduling bottlenecks (blockages and starvation).
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Source: Lopes et al. (2016). (Color figure online)
Source: Lopes et al. (2016)
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Notes
The value 250 time units is employed based on the optimal processing time from answers obtained by other formulations.
The value 160 time units is employed based on observed cycle time values of other formulations.
Horizontal balancing HX is not tested due to its poor performance on the practical case study and to its non-linearities that prevent optimal solutions from being found.
In an MPS of five units (1, 1, 1, 1, 1), by fixating the first model in the first position, one can generate 4! combinations of cyclical sequences. Each sequence requires a quick simulation of a few replications of the MPS going through the line. Alternatively, linear relaxations of the proposed model can be used.
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Acknowledgements
The authors would like to thank the financial support from Fundação Araucária—Agreements 141/2015, 06/2016 and 041/2017 FA-UTFPR-RENAULT, and CNPq (Grant 406507/2016-3).
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Lopes, T.C., Sikora, C.G.S., Michels, A.S. et al. Mixed-model assembly lines balancing with given buffers and product sequence: model, formulation comparisons, and case study. Ann Oper Res 286, 475–500 (2020). https://doi.org/10.1007/s10479-017-2711-0
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DOI: https://doi.org/10.1007/s10479-017-2711-0