Efficient algorithms for flexible job shop scheduling with parallel machines
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Bibliographic record
Abstract
Abstract Job shop scheduling with a bank of machines in parallel is important from both theoretical and practical points of view. Herein we focus on the scheduling problem of minimizing the makespan in a flexible two‐center job shop. The first center consists of one machine and the second has k parallel machines. An easy‐to‐perform approximate algorithm for minimizing the makespan with one‐unit‐time operations in the first center and k ‐unit‐time operations in the second center is proposed. The algorithm has the absolute worst‐case error bound of k − 1 , and thus for k = 1 it is optimal. Importantly, it runs in linear time and its error bound is independent of the number of jobs to be processed. Moreover, the algorithm can be modified to give an optimal schedule for k = 2 .
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it