Mathematical programming modelling of the response time variability problem
Bibliographic record
Abstract
The Response Time Variability Problem (RTVP) is a scheduling problem that has recently been defined in the literature. The RTVP has a broad range of real-life applications. For example, in the automobile industry it an be used to sequence the models to be produced on a mixed-model assembly line. A previous study developed a position exchange heuristic to apply to certain greedy initial sequences for the RTVP. Some mathematical programming models (MILPs) have also been tested to solve it to optimality, but the practical limit to obtaining optimal solutions is 25 units to be scheduled. This paper aims to improve the best mathematical programming model developed thus far in order to solve larger instances up to 40 units to optimality. The contribution of this paper is threefold: i) larger instances can be solved to optimality; ii) the new optimal solution of the RTVP can be used to compare the results of heuristics procedures; and iii) the importance of modelling is demonstrated, as well as the huge impact that reformulation, redundant constraints and the elimination of symmetries have on efficiency of MILPs.
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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 | 0.002 | 0.004 |
| 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 | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 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".