Revisit the Scheduling Problem with Calibrations
Bibliographic record
Abstract
The research about scheduling with calibrations was initiated from the Integrated Stockpile Evaluation (ISE) program which tests nuclear weapons periodically. The tests for these weapons require calibrations that are expensive in the monetary sense. This model has many industrial applications where the machines need to be calibrated periodically to ensure high-quality products, including robotics and digital cameras. In 2013, Bender et al. (SPAA '13) proposed a theoretical framework for the ISE problem. In this model, a machine can only be trusted to run a job when it is calibrated and the calibration remains valid for a time period of length T, after which it must be recalibrated before running more jobs. The objective is to find a schedule that completes all jobs by their deadlines and minimizes the total number of calibrations. In this paper, we study the scheduling problem with calibrations on multiple parallel machines where we consider unit-time processing jobs with release times and deadlines. We propose a dynamic programming algorithm with polynomial running time when the number of machines is constant. Then, we propose another dynamic programming approach with polynomial running time when the length of the calibrated period is constant. Also, we propose a PTAS, that is, for any constant ε > 0, we give a (1+ε) - approximation solution with m machines.
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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 | 0.003 | 0.009 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.009 | 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".