Branch-Price-and-Cut Algorithms for the Pickup and Delivery Problem with Time Windows and Last-in-First-Out Loading
Bibliographic record
Abstract
This paper proposes models and algorithms for the pickup and delivery vehicle routing problem with time windows and last-in-first-out (LIFO) loading constraints (PDPTWL). The LIFO loading rule ensures that no handling is required prior to unloading an item from a vehicle: a linear stack loading structure is maintained and an item can only be delivered if it is the last one in the stack. Three exact branch-price-and-cut algorithms are proposed for this problem. The first incorporates the LIFO constraints in the master problem. The second one handles the LIFO constraints directly in the shortest path pricing problem. It applies a dynamic programming algorithm relying on an ad hoc dominance criterion. The third algorithm is a hybrid between the first two methods. Known valid inequalities are adapted to the PDPTWL and the impact of different path relaxations on the total computation time is investigated. Computational results obtained on instances derived from known instances of the pickup and delivery problem with time windows (PDPTW) are reported.
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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 | 0.006 |
| 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) | 0.010 | 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".