Multicommodity Production Planning: Qualitative Analysis and Applications
Bibliographic record
Abstract
We develop a qualitative analysis theory for the convex-cost dynamic multicommodity production planning problem, which can be used, without performing any computational work, to provide invaluable insight to managers when faced with the task of deciding how to respond to changes in problem environment. We first formulate the problem as a multicommodity flow problem with parameters associated with each arc–commodity pair. We then reduce the problem to an equivalent single-commodity flow problem and develop a complete characterization of conformality among production, sales, and inventory activities in various instances of the problem. By combining the conformality characterizations with the monotonicity theory of Granot and Veinott [Granot F, Veinott AF Jr (1985) Substitutes, complements and ripples in network flow. Math. Oper. Res. 10:471–497] for single-commodity problems, we study the effects of changes in problem environment on optimal production, sales, and inventory schedules in the multicommodity problem. Numerous applications are presented and analyzed.
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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 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.002 |
| 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".