Integrated design of supply chain networks with three echelons, multiple commodities and technology selection
Bibliographic record
Abstract
We consider a strategic supply chain design problem with three echelons, multiple commodities and technology selection. We model the problem as a tri-echelon, capacitated facility location problem that decides on the location of plants and warehouses, their capacity and technology planning, the assignment of commodities to plants and the flow of commodities to warehouses and customer zones. We use a mixed-integer programming formulation strengthened by valid but redundant constraints and apply Lagrangean relaxation to decompose the problem by echelon. Lagrangean relaxation provides a lower bound that is calculated using an interior-point cutting plane method. Feasible solutions are generated using a primal heuristic that uses the solution of the subproblems. Unlike common practice in the literature, the decomposition does not aim at getting easy subproblems, but rather at getting subproblems that preserve most of the characteristics of the original problem. Not only does this provide a sharp lower bound but also leads to a simple and efficient primal heuristic. We can afford to have relatively difficult subproblems because the interior-point cutting plane method used to solve the Lagrangean dual makes clever and selective choices of the Lagrangean multipliers leading to fewer calls to the subproblems. Computational results indicate the efficiency of the approach in providing a sharp bound and in generating feasible solutions that are of high quality.
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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 | 0.001 | 0.002 |
| 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 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".