Fair cost savings allocation in two-stage fixed-cost transportation problem
Bibliographic record
Abstract
This paper navigates the economic efficiency in a two-stage fixed-cost transportation problem (TS-FCTP), employing cooperative game theory (CGT) for fair allocation in a shared transportation network. Collaboration among Logistics Service Providers (LSPs) in a multi-echelon supply chain network, such as in TS-FCTP, emerges as a pivotal strategy to reduce costs and enhance network efficiency. The allocation of these cost savings among LSPs becomes a crucial question, prompting the introduction of a transportation game (TG) with LSPs as players. Diverse CGT solution concepts are explored to distribute cost savings among participating LSPs. We consider both synthetic and real datasets. For these datasets, we notice that the transportation game is monotonic and superadditive, and the core is non-empty. These properties indicate the willingness of players to form a coalition. Additionally, we determine the most stable cost savings allocation using the core center concept. The optimal coalition formation sequence has been identified using the Shapley monotonic path. Our findings illustrate that LSPs bear lower costs when cooperating with other LSPs. In this TG, individual players’ utility is computed by solving a TS-FCTP. This can be computationally intensive, even for medium-sized problem instances. We propose two valid inequalities (VIs) that significantly reduce the computation time.
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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 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| 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".