Logic-based Benders Decomposition for Alternative Resource Scheduling with Sequence Dependent Setups
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Bibliographic record
Abstract
We study an unrelated parallel machines scheduling problem with sequence and machine dependent setup times. A logic-based Benders decomposition approach is proposed to minimize the makespan. This approach is a hybrid model that makes use of a mixed integer programming master problem and a specialized solver for travelling salesman subproblems. The master problem is used to assign jobs to machines while the subproblems obtain optimal schedules on each machine given the master problem assignments. Computational results show that the Benders model is able to find optimal solutions up to six orders of magnitude faster as well as solving problems six times the size previously possible with a mixed integer programming model in the literature and twice the size that a branchand-bound algorithm can solve for similar problems. We further relax the Benders decomposition to accept suboptimal schedules and demonstrate the ability to parameterize solution quality while out-performing state-of-the-art metaheuristics both in terms of solution quality and mean run-time.
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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 | 0.000 | 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