Minimizing makespan in a three-stage hybrid flow shop with dedicated machines
Why this work is in the frame
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Bibliographic record
Abstract
In recent years, many studies on scheduling problems with dedicated machines have been carried out. But, few of them have considered the case of more than two stages. This paper aims at filling this gap by addressing the three-stage hybrid flow shop scheduling problem with two dedicated machines in stage 3. Each job must be processed, consecutively, on the single machines of stages 1 and 2, and depending on its type, it will be further processed on one of the two dedicated machines of stage 3. The objective is to find an optimal schedule that minimizes the maximum completion time (makespan). Since this problem is strongly NP-hard, we first provide some basic results including solutions for several variations of the problem. Then, for the general case we adapt a set of lower bounds from the literature and propose a heuristic approach that is based on the dynamic programming technique, which uses a local search procedure. Finally, various experimentations on several problems with different sizes are conducted and the computational results of the heuristic show that the mean percentage deviation value from the lower bound was lower than 0.8 percent for some instances with 40 to 200 jobs in size.
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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