Mechanisms for feasibility and improvement for inventory-routing problems
Bibliographic record
Abstract
Inventory-routing problems (IRPs) define a class of combinatorial optimization problems, encompassing inventory management and vehicle routing decisions into the same framework. In this article, we propose a new modular mechanism capable of recovering feasibility and improving even partial solutions by reorganizing delivery routes and optimizing inventory flows. It can be embedded into different optimization algorithms, either heuristic or exact ones. We exploit the use of this mechanism to improve a traditional branch-and-cut scheme and evaluate it by solving the multi-vehicle IRP (MIRP) and the multi-depot IRP (MDIRP). The results show that our method is very effective; outperforming other approaches on well-known benchmark instances from the literature. Regarding the MIRP, our algorithm obtains 417 optimal solutions for 638 small instances, the best result among all exact algorithms, with nine new ones. On a large data set, our method finds all optimal solutions for instances with up to 50 customers for the single-vehicle, besides providing 90% of new best-known solutions (BKS) for 100 customers. On the MDIRP, our approach finds 27 new optimal solutions and 73% of new BKS, improving previous BKS by more than 7% on average.
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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 | 0.014 | 0.029 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.006 |
| Open science | 0.005 | 0.005 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.008 | 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".