Revisiting Johnson's rule for minimizing makespan in the Two-Machine Flow Shop scheduling problem
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908751634628608 |
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| author | Della Croce, Federico Schau, Quentin |
| author_facet | Della Croce, Federico Schau, Quentin |
| contents | We consider Johnson's rule for minimizing the makespan in the two-machine flow shop problem. Although its worst-case time complexity is O(n log n), we show that it is possible to detect in linear time whether a full sorting of jobs can be avoided and an optimal solution can be computed in O(n) time. A probabilistic analysis indicates that linear time complexity holds with high probability under uniformly distributed processing times, a result further supported by extensive computational experimentation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06119 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Revisiting Johnson's rule for minimizing makespan in the Two-Machine Flow Shop scheduling problem Della Croce, Federico Schau, Quentin Optimization and Control 90 We consider Johnson's rule for minimizing the makespan in the two-machine flow shop problem. Although its worst-case time complexity is O(n log n), we show that it is possible to detect in linear time whether a full sorting of jobs can be avoided and an optimal solution can be computed in O(n) time. A probabilistic analysis indicates that linear time complexity holds with high probability under uniformly distributed processing times, a result further supported by extensive computational experimentation. |
| title | Revisiting Johnson's rule for minimizing makespan in the Two-Machine Flow Shop scheduling problem |
| topic | Optimization and Control 90 |
| url | https://arxiv.org/abs/2512.06119 |