A mixed‐integer programming approach for clustering demand data for multiscale mathematical programming applications
Bibliographic record
Abstract
Abstract Across all sectors within the energy and process industry, tremendous efforts have been devoted toward the development and operation of agile manufacturing techniques to respond to customer needs and volatile markets while at the same time control costs, improve efficiency, and reduce pollution. This has created a demand for systems to solve complex integrated planning and scheduling problems that bridge the gap between the different functional and strategic decision‐making levels. Integration across supply chain decision levels is key to improving investment returns. Different approaches have been proposed to tackle this problem. However, most of them are problem‐specific or applicable only to short time horizons. Clustering has the potential to handle such problems by grouping similar input parameters together and considerably reduce the model size while not compromising solution accuracy. This work presents a new class of clustering algorithms to support the integration of planning applications of different time scales. The clustering algorithms were formulated using integer programming with integral absolute error as similarity measure. The algorithms were successfully applied to clustering electricity demand data and applied to the unit commitment problem. The computational performances of the proposed normal and sequence clustering algorithms were compared against a full planning model that does not employ clustering. The results show a clear advantage in terms of solution time compared to the full‐scale case while maintaining solution accuracy.
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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 | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".