Decomposition Methods for the Parallel Machine Scheduling Problem with Setups
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Bibliographic record
Abstract
We study the unrelated parallel machine scheduling problem with sequence and machine-dependent setup times and the objective of makespan minimization. Two exact decomposition-based methods are proposed based on logic-based Benders decomposition and branch and check. These approaches are hybrid models that make use of a mixed-integer programming (MIP) master problem and a specialized solver for travelling salesman subproblems. The master problem is used to assign jobs to machines, whereas the subproblems find optimal schedules on each machine given the master problem assignments. Computational results show that the decomposition models are able to find optimal solutions up to four orders of magnitude faster than the existing state of the art as well as solve problems six times larger than an existing MIP model. We further investigate the solution quality versus runtime trade-off for large problem instances for which the optimal solutions cannot be found and proved in a reasonable time. We demonstrate that the branch-and-check hybrid algorithm is able to produce better schedules in less time than the state-of-the-art metaheuristic, while also providing an optimality gap.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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