Hub-and-Spoke Network Design Considering Congestion and Flow-Based Cost Function
Bibliographic record
Abstract
This paper presents a model for a “hub-and-spoke network design considering congestion and flow-based cost function”. The number of hubs and spokes is unknown, and the objective is to minimize the cost (including the transportation cost, lost demand, and facility setup cost). In the post-pandemic era, it is expected to have government-imposed restrictions on the congestion of airports, as a measure of health and safety. Unlike the current literature which considers a monetary penalty for congestion, we consider congestion as an externally imposed factor, which should be modeled as a constraint. We take a gravity-based modeling approach to obtain the desirability of a facility and calculate the demand matrix of the network. To solve the model, a Benders decomposition approach is proposed. Without the Benders decomposition approach, only instances with up to ten nodes were solved within a reasonable time, but with the Benders decomposition approach, instances with up to forty nodes were solved. A heuristic algorithm is developed to have a mechanism for dealing with larger instances. A set of experiments are conducted using data from the Turkish Network dataset to study various aspects of the proposed formulation and different parameters’ effects on the performance of the model.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.003 | 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".