Abstract
Human labor is generally being replaced with robots for high automation, increased flexibility, and reduced costs in modern industry. Few studies consider the sequence-dependent setup times in the assembly line balancing literature. However, it should not be overlooked in a real-life setting. This article presents a new mathematical model and variable neighborhood search (VNS) algorithm for mixed-model robotic two-sided assembly line balancing, with the aim of minimizing the cycle time by considering the sequence-dependent setup times. The effectiveness of the proposed VNS is tested with a set of test problems from the literature. The computational results and statistical analysis indicate that the proposed method yields promising results.
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Appendix
Appendix
1.1 Appendix A: Sequence-dependent setup times
Sequence-dependent setup times of model A are as follows:
Robot 1 | Robot 2 | ||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 0.2 | 0.5 | 0.3 | 0.4 | 0.3 | 0.2 | 0.2 | 0.4 | 0 | 0.3 | 0.2 | 0.3 | 0.5 | 0.5 | 0 | 0.1 | 0.5 |
0 | 0 | 0.5 | 0.5 | 0.4 | 0.5 | 0.5 | 0.5 | 0.4 | 0.5 | 0 | 0.4 | 0.1 | 0.5 | 0.2 | 0.3 | 0.2 | 0.5 |
0.4 | 0.5 | 0 | 0.4 | 0.2 | 0.1 | 0.5 | 0.2 | 0.5 | 0.2 | 0 | 0 | 0 | 0 | 0 | 0.1 | 0.3 | 0.5 |
0.2 | 0.5 | 0.5 | 0 | 0.6 | 0.2 | 0.1 | 0.2 | 0.2 | 0.5 | 0.5 | 0.1 | 0 | 0.5 | 0.3 | 0.3 | 0.2 | 0.4 |
0.1 | 0 | 0.3 | 0.3 | 0 | 0.3 | 0.2 | 0.1 | 0.1 | 0.6 | 0.3 | 0.5 | 0.4 | 0 | 0.2 | 0.5 | 0 | 0.3 |
0.4 | 0.3 | 0 | 0.6 | 0.1 | 0 | 0.5 | 0.4 | 0 | 0 | 0.4 | 0.4 | 0.3 | 0.3 | 0 | 0.2 | 0.4 | 0.6 |
0 | 0.3 | 0.3 | 0.3 | 0.3 | 0.3 | 0 | 0.1 | 0.6 | 0.6 | 0.2 | 0.1 | 0.4 | 0.4 | 0.6 | 0 | 0.6 | 0.3 |
0.5 | 0.4 | 0.2 | 0.6 | 0.4 | 0.3 | 0.6 | 0 | 0.6 | 0.3 | 0.5 | 0.1 | 0.5 | 0.1 | 0.1 | 0.4 | 0 | 0.5 |
0.5 | 0.1 | 0.2 | 0.1 | 0.5 | 0.6 | 0.4 | 0.1 | 0 | 0.5 | 0.2 | 0.2 | 0.5 | 0.1 | 0.1 | 0.1 | 0.2 | 0 |
Robot 3 | Robot 4 | ||||||||||||||||
0 | 0.2 | 0.2 | 0.4 | 0.1 | 0.3 | 0 | 0.5 | 0.3 | 0 | 0.3 | 0.2 | 0.1 | 0.2 | 0.1 | 0 | 0.3 | 0.4 |
0.2 | 0 | 0.4 | 0.5 | 0.4 | 0.2 | 0.2 | 0.5 | 0.1 | 0.6 | 0 | 0.3 | 0.3 | 0.1 | 0.3 | 0.3 | 0.5 | 0.3 |
0.1 | 0.3 | 0 | 0.3 | 0.5 | 0.2 | 0.5 | 0.1 | 0.6 | 0.2 | 0.4 | 0 | 0.4 | 0 | 0.3 | 0.6 | 0.3 | 0.6 |
0 | 0 | 0.4 | 0 | 0.3 | 0.6 | 0.6 | 0.2 | 0.3 | 0.3 | 0 | 0.1 | 0 | 0.3 | 0.5 | 0 | 0.2 | 0.1 |
0.5 | 0.3 | 0.2 | 0.2 | 0 | 0.1 | 0.2 | 0.1 | 0.4 | 0.3 | 0.3 | 0.1 | 0 | 0 | 0.6 | 0.5 | 0.3 | 0.2 |
0.1 | 0.4 | 0.6 | 0.1 | 0.6 | 0 | 0.2 | 0.2 | 0.2 | 0.2 | 0 | 0.2 | 0.5 | 0.6 | 0 | 0.1 | 0.5 | 0.1 |
0.1 | 0.2 | 0.1 | 0.4 | 0.6 | 0.4 | 0 | 0.2 | 0.5 | 0.5 | 0.3 | 0.2 | 0.5 | 0.4 | 0.5 | 0 | 0.3 | 0.4 |
0 | 0.5 | 0.1 | 0.5 | 0.6 | 0.2 | 0.1 | 0 | 0.4 | 0.4 | 0.3 | 0.5 | 0.4 | 0.6 | 0.4 | 0.3 | 0 | 0.3 |
0.6 | 0.4 | 0.6 | 0.4 | 0.5 | 0.1 | 0.1 | 0.5 | 0 | 0.5 | 0.3 | 0.1 | 0 | 0 | 0.5 | 0.5 | 0.3 | 0 |
Sequence-dependent setup times of model B are as follows:
Robot 1 | Robot 2 | ||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 0.3 | 0.1 | 0.5 | 0.4 | 0.3 | 0.2 | 0.4 | 0.6 | 0 | 0.2 | 0.6 | 0.1 | 0.6 | 0.4 | 0.5 | 0.5 | 0.1 |
0 | 0 | 0.2 | 0.4 | 0.4 | 0.1 | 0.3 | 0.4 | 0.5 | 0.1 | 0 | 0.3 | 0.5 | 0.2 | 0.3 | 0.5 | 0.2 | 0.1 |
0.5 | 0.2 | 0 | 0.3 | 0 | 0.4 | 0 | 0.5 | 0.1 | 0.4 | 0.5 | 0 | 0.3 | 0.5 | 0.4 | 0.3 | 0.1 | 0.4 |
0.5 | 0.1 | 0.5 | 0 | 0.5 | 0.6 | 0.2 | 0.5 | 0.4 | 0.4 | 0.1 | 0.6 | 0 | 0.2 | 0.6 | 0.1 | 0.5 | 0.4 |
0.4 | 0.4 | 0.5 | 0.1 | 0 | 0.3 | 0.5 | 0.1 | 0.6 | 0.3 | 0.4 | 0.1 | 0.1 | 0 | 0.3 | 0 | 0.2 | 0.2 |
0.3 | 0.2 | 0.2 | 0.1 | 0 | 0 | 0.3 | 0.2 | 0.5 | 0.3 | 0.2 | 0.6 | 0.2 | 0.2 | 0 | 0.1 | 0.2 | 0 |
0.2 | 0.3 | 0.4 | 0.2 | 0.3 | 0.5 | 0 | 0.3 | 0.5 | 0.3 | 0.4 | 0.2 | 0.1 | 0.1 | 0.6 | 0 | 0.1 | 0.5 |
0.6 | 0.1 | 0 | 0.5 | 0.4 | 0.3 | 0.2 | 0 | 0.2 | 0.3 | 0.1 | 0.2 | 0.2 | 0.3 | 0.5 | 0.2 | 0 | 0.5 |
0.4 | 0.3 | 0.4 | 0.5 | 0.3 | 0.5 | 0.6 | 0.5 | 0 | 0.1 | 0.4 | 0.6 | 0.2 | 0.5 | 0.4 | 0.3 | 0.5 | 0 |
Robot 3 | Robot 4 | ||||||||||||||||
0 | 0.5 | 0 | 0.1 | 0.2 | 0.4 | 0.1 | 0.5 | 0.5 | 0 | 0.3 | 0.3 | 0 | 0.2 | 0.6 | 0.3 | 0.3 | 0.4 |
0.1 | 0 | 0.1 | 0.1 | 0.4 | 0.6 | 0.4 | 0 | 0.3 | 0.1 | 0 | 0.1 | 0.3 | 0.6 | 0.3 | 0.2 | 0.4 | 0.1 |
0.3 | 0.5 | 0 | 0.4 | 0.4 | 0.5 | 0.1 | 0.3 | 0.3 | 0.5 | 0.6 | 0 | 0.6 | 0.3 | 0 | 0.3 | 0.3 | 0.6 |
0.6 | 0.5 | 0.1 | 0 | 0.2 | 0.2 | 0.3 | 0.1 | 0.2 | 0.6 | 0.3 | 0.3 | 0 | 0.5 | 0.1 | 0.4 | 0.4 | 0.5 |
0.6 | 0.1 | 0.4 | 0.5 | 0 | 0 | 0.1 | 0.1 | 0.1 | 0.1 | 0.5 | 0.4 | 0.3 | 0 | 0.4 | 0.5 | 0.2 | 0.6 |
0.1 | 0.4 | 0.1 | 0.4 | 0.3 | 0 | 0.2 | 0.2 | 0.2 | 0.3 | 0.3 | 0.3 | 0.3 | 0.1 | 0 | 0.6 | 0 | 0.5 |
0.4 | 0.5 | 0.4 | 0 | 0.3 | 0.1 | 0 | 0.5 | 0.3 | 0.6 | 0.3 | 0.5 | 0.3 | 0.4 | 0.4 | 0 | 0.5 | 0 |
0.6 | 0.2 | 0.4 | 0.1 | 0.6 | 0.1 | 0.5 | 0 | 0 | 0.4 | 0.6 | 0.5 | 0.3 | 0.5 | 0.4 | 0.3 | 0 | 0.5 |
0.2 | 0.2 | 0.3 | 0.4 | 0.1 | 0.2 | 0.1 | 0.4 | 0 | 0.2 | 0.3 | 0.1 | 0 | 0 | 0.3 | 0.3 | 0.3 | 0 |
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Aslan, Ş. Mathematical model and a variable neighborhood search algorithm for mixed-model robotic two-sided assembly line balancing problems with sequence-dependent setup times. Optim Eng 24, 989–1016 (2023). https://doi.org/10.1007/s11081-022-09718-3
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DOI: https://doi.org/10.1007/s11081-022-09718-3