Branch-price-and-cut algorithms for the pickup and delivery problem with time windows and multiple stacks
Bibliographic record
Abstract
This paper proposes models and algorithms for the pickup and delivery vehicle routing problem with time windows and multiple stacks. Each stack is rear-loaded and is operated in a last-in-first-out (LIFO) fashion, meaning that when an item is picked up, it is positioned at the rear of a stack. An item can only be delivered if it is in that position. This problem arises in the transportation of heavy or dangerous material where unnecessary handling should be avoided, such as in the transportation of cars between car dealers and the transportation of livestock from farms to slaughterhouses. To solve this problem, we propose two different branch-price-and-cut algorithms. The first solves the shortest path pricing problem with the multi-stack policy, while the second incorporates this policy partly in the shortest path pricing problem and generates additional inequalities to the master problem when infeasible multi-stack routes are encountered. Computational results obtained on instances derived from benchmark instances for the pickup and delivery traveling salesman problem with multiple stacks are reported, and reveal the advantage of incorporating the multi-stack policy in the pricing problem. Instances with up to 75 requests and with one, two and three stacks can be solved optimally within 2 hours of computational time.
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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 | 0.003 | 0.005 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.003 | 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".