Mathematical programming in public bus transit design and operations: Emerging technologies and sustainability – A review
Bibliographic record
Abstract
Public bus transit service (PBTS) is recognized as a highly effective mode of transportation, offering accessibility, affordability, and adaptability that contribute to its critical role in transportation networks. The extensive literature on PBTS encompasses various aspects, with mathematical programming emerging as a widely employed methodology to tackle the public bus transit network design and operations planning problem (PBTNDP&OPP). In this paper, first, we employ the critical path method (CPM) to visually map the development of existing literature on the application of mathematical programming in PBTND&OPP by focusing on manuscripts published in top-tier journals. The objective is to identify key sub-problems extensively studied in the literature and recently emerging topics. Then, we conduct a comprehensive review of recent applications of mathematical programming in PBTND&OPP, encompassing sustainable and green practices, as well as emerging transportation technologies and modes within PBTS. These two sub-problems have been identified as recently emerged and hot topics in the literature of mathematical programming and PBTND&OPP, based on the provided CPM in the first step. Selected papers for each sub-problem are examined, providing insights into problem formulation, objective functions, decision variables, demand patterns, network structures, and key findings. Based on the literature review, we systematically identify research gaps in each sub-problem and offer directions and suggestions for future studies. While there is a considerable body of literature that has applied mathematical programming to investigate these two emerging topics, our review highlights that the existing literature is still in the early stages of development. Hence, numerous problems relating to these topics remain ripe for exploration through mathematical programming. Examining the effects of sustainable development policies or the introduction of emerging technologies on the reliability and long-term performance of PBTSs represents a significant gap in current research. On the methodological side, the main gap in the literature is the absence of efficient hybrid approaches, where mathematical programming is integrated with other approaches to provide more robust results and to capture the dynamics of PBTSs. Our work aims to advance knowledge in the field of PBTND&OPP and inspire further research endeavors.
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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 | 0.003 | 0.007 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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".