Intermodal Hub Network Design with Probabilistic Service-Level Constraints
Bibliographic record
Abstract
In this paper, we study the intermodal hub network design problem with probabilistic service-level constraints ensuring that total service time requirements of customers’ orders are satisfied with a minimum probability. The intermodal network is modeled as a Jackson queueing network with [Formula: see text] queues for the hubs and [Formula: see text] queues for transport operations. We characterize the total service time distribution and propose a cutting-plane algorithm that exploits the characteristics of this distribution. We show that the α-level sets of the total sojourn time distribution for a transport path including two or more hubs are homothetic with some homothetic center. This characteristic allows for the derivation of valid inequalities leading to significant reductions in the solution time. We propose a worst-case renewal approximation considering [Formula: see text] queues to extend our analysis to non-Jackson networks. We prove that the properties of the total sojourn time distribution derived for Jackson networks also hold for this renewal approximation, allowing the application of the derived cutting-plane approach to the general case. Extensive computational experiments are performed on the Australian Post and Colombian data sets to assess the performance of the proposed formulations and solution algorithms. Funding: The authors acknowledge support from the Natural Sciences and Engineering Research Council of Canada. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2024.0657 .
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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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 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 | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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".