Many to many hub and spoke location routing problem based on the gravity rule
Bibliographic record
Abstract
This paper examines the spoke and hub location decisions in a routing problem.To minimize the total cost, the study analyzes on how to locate the spokes, hubs and the allocation of spoke nodes to hub nodes, the routing among the nodes and the number of vehicles assigned to each hub thoroughly.As there might be no facility assigned to some points, unsatisfied demands must be distributed to other nodes with available facilities.Furthermore, the realized demand is determined by considering the perceived utility of each path, using The Gravity rule.For this purpose, the proposed nonlinear model is transformed into a linear programming model, where some tightening rules and preprocessing procedures are applied, and also the sequential and integrated approaches are developed to solve the problem.In the sequential method, spokes are allocated, and hubs are selected based on the location of the spokes, after which the routing in the local tour is determined.Meanwhile, in the integrated approach, the aggregated model is solved.A heuristic is presented to address the integrated model.Numerical experiments are run on both approaches, to compare both, and obtain insights from 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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 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 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".