Benders Decomposition for Production Routing under Demand Uncertainty
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Bibliographic record
Abstract
The production routing problem (PRP) is a generalization of the inventory routing problem and concerns the production and distribution of a single product from a production plant to multiple customers using capacitated vehicles in a discrete- and finite-time horizon. In this study, we consider the stochastic PRP with demand uncertainty in two-stage and multistage decision processes. The decisions in the first stage include production setups and customer visit schedules, while the production and delivery quantities are determined in the subsequent stages. We introduce formulations for the two problems, which can be solved by a branch-and-cut algorithm. To handle a large number of scenarios, we propose a Benders decomposition approach, which is implemented in a single branch-and-bound tree and enhanced through lower-bound lifting inequalities, scenario group cuts, and Pareto-optimal cuts. For the multistage problem, we also use a warm start procedure that relies on the solution of the simpler two-stage prob...
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it