A Computational Study of Continuous and Discrete Time Formulations for a Class of Short-Term Scheduling Problems for Multipurpose Plants
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Bibliographic record
Abstract
A key decision in scheduling problems is deciding when to perform certain operations, and the quality of solutions depends on how time is represented. The two main classes of time representation are discrete-time approaches (with uniform or nonuniform discretization schemes) and continuous-time approaches. In this work, we compare the performance of these two classes for short-term scheduling of multipurpose facilities with single purpose machines, constant processing times, discrete batches, material splitting, multitasking, and no batch mixing. In addition, the different discretization schemes were compared against each other. We show that, for the modeling framework proposed in this work, the selected discrete-time formulation typically obtained higher quality solutions, and required less time to solve as compared to the selected continuous-time formulation, as the continuous-time formulation exhibited detrimental trade-off between computational time and solution quality. We also show that within the scope of this study, nonuniform discretization schemes typically yielded solutions of similar quality as compared to a fine uniform discretization scheme, but required only a fraction of the computational time. A total of 190 small and industrial-sized instances, comprised of 1030 runs, were considered for this study.
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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 | 0.001 |
| 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