Mathematical formulations for multi-period network design with modular capacity adjustments
Bibliographic record
Abstract
Network design problems are at the heart of several applications in domains such as transportation, telecommunication, energy and natural resources. This paper proposes a new multi-period network design problem variant, in which modular capacities can be added or reduced along the planning horizon in order to adapt to demand changes. The problem further allows to represent economies of scales in function of the total arc capacity, a detail that has typically been overlooked in the literature. This paper particularly emphasizes the different alternatives to formulate the problem. We propose two different mixed-integer programming formulations and analyze further modeling alternatives. We theoretically compare the strength of all formulations and evaluate their computational performance in extensive experiments. The results suggest that a recent modeling technique using more precise decision variables yields the strongest formulation, which also results in significantly faster solution times. The use of this formulation may therefore be beneficial when considering similar problem variants. Finally, we also evaluate the economical benefits of the features introduced in this new problem variant, indicating that both the selection of the capacity levels and the capacity adjustment along time are likely to result in significant cost savings.
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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 | 0.003 | 0.004 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.007 | 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".