Lagrangean‐based solution approaches for the generalized problem of locating capacitated warehouses
Bibliographic record
Abstract
Abstract The traditional capacitated warehouse location problem consists of determining the number and the location of capacitated warehouses on a predefined set of potential sites such that the demands of a set of customers are met. A very common assumption made in modeling this problem in almost all of the existing research is that the total capacity of all potential warehouses is sufficient to meet the total demand. Whereas this assumption facilitates to define a well‐structured problem from the mathematical modeling perspective, it is in fact restrictive, not realistic, and hence rarely held in practice. The modeling approach presented in this paper breaks away from the existing research in relaxing this very restrictive assumption. This paper therefore investigates the generalized problem of locating warehouses in a supply chain setting with multiple commodities with no restriction on the total capacity and the demand. A new integer programming formulation for this problem is presented, and an algorithm based on Lagrangean relaxation and decomposition is described for its solution. Three Lagrangean heuristics are proposed. Computational results indicate that reasonably good solutions can be obtained with the proposed algorithms, without having to use a general purpose optimizer.
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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 | 0.003 |
| 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 | 0.001 | 0.001 |
| Open science | 0.002 | 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".