Logic-based Benders Decomposition for Alternative Resource Scheduling with Sequence Dependent Setups
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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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".