The Capacitated <i>p</i>‐facility Location Problem on the Real Line
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
The problem we address involves locating p new facilities to service a set of customers or fixed points on the real line such that a measure of total cost will be minimized. A basic form of this problem was investigated by Love (1976), who observed that the fixed points must be allocated in sequence to the new facilities in an optimal solution, and thus, the problem can be solved by a dynamic programming algorithm. Since then, other forms of the model have been investigated; however, in all cases it is assumed that the new facilities have unlimited capacity so that customer flows are always allocated to the nearest facility. The objective of this paper is to analyze the effect of capacity constraints on the optimal locations of the new facilities. A general fixed‐cost function is also included to account for practical considerations such as zoning regulations, and to permit the facilities to be located anywhere on the line instead of only at the fixed vertices. A dynamic programming method is formulated to solve the problem when the variable cost components are increasing convex functions of travel distance. The problem is shown to be NP‐hard under more general cost structures.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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 it