A Due-Window Determination In Minmax Scheduling Problems
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Bibliographic record
Abstract
In several recent scheduling studies the notion of due-date is generalized: it is assumed that jobs completed within a certain time interval (rather than at a time point) are considered as being on time, whereas jobs completed outside this interval are penalized. We study a scheduling problem on parallel identical machines, in which the schedule as well as the common due-window are to be determined. The relevant cost components are: maximum earliness, maximum tardiness, due-window starting time and due-window length. The objective is of a minmax type, i.e. we look for the schedule and due-window with minimum cost of the worst scheduled job, with respect to all cost components. We solve the problem to optimality on a single machine, and we introduce an efficient (and asymptotically optimal) heuristic algorithm and a simple lower bound for the general multi-machine case. An extension to non-linear cost functions as well as the special case of unit processing times are also studied. We conclude with an extensive numerical study which indicates that both the heuristic and the lower bound produce very close-to-optimal results under various job and machine environments.
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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 | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.002 |
| 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