A Logic-Based Benders Approach to Scheduling with Alternative Resources and Setup Times
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Bibliographic record
Abstract
We study an unrelated parallel machines scheduling problem with sequence and machine dependent setup times. A logicbased Benders decomposition approach is proposed to minimize the makespan. The decomposition approach is a hybrid model that makes use of a mixed integer programming master problem and a travelling salesman problem subproblem. The master problem is a relaxation of the problem and is used to create assignments of jobs to machines, while the subproblem obtains optimal schedules based on the master problem assignments. Computational results comparing the Benders decomposition and mixed integer program formulation show that the Benders model is able to find optimal solutions to problems up to five orders of magnitude faster as well as solving problems four times the size possible previously.
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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