Transshipment prices and pair-wise stability in coordinating the decentralized transshipment problem
Bibliographic record
Abstract
The decentralized transshipment problem is a two-stage decision making problem where the companies first choose their individual production levels in anticipation of random demands and after demand realizations they pool residuals via transshipment. The coordination will be achieved if at optimality all the decision variables, i.e. production levels and transshipment patterns, in the decentralized system are the same as those of centralized system. In this paper, we study the coordination via transshipment prices. We propose a procedure for deriving the transshipment prices based on the coordinating allocation rule introduced by Anupindi et al. [1]. With the transshipment prices being set, the companies are free to match their residuals based on their individual preferences. We draw upon the concept of pair-wise stability to capture the dynamics of corresponding matching process. As the main result of this paper, we show that with the derived transshipment prices, the optimum transshipment patterns are always pair-wise stable, i.e. there are no pairs of companies that can be jointly better off by unilaterally deviating from the optimum transshipment patterns.
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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 | 0.012 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".