An Integer <i>L</i>-Shaped Algorithm for the Capacitated Vehicle Routing Problem with Stochastic Demands
Bibliographic record
Abstract
The classical Vehicle Routing Problem consists ofdetermining optimal routes for m identical vehicles, starting and leaving at the depot, such that every customer is visited exactly once. In the capacitated version (CVRP) the total demand collected along a route cannot exceed the vehicle capacity. This article considers the situation where some ofthe demands are stochastic. This implies that the level of demand at each customer is not known before arriving at the customer. In some cases, the vehicle may thus be unable to load the customer's demand, even ifthe expected demand along the route does not exceed the vehicle capacity. Such a situation is referred to as a failure. The capacitated vehicle routing problem with stochastic demands (SVRP) then consists ofminimizing the total cost ofthe planned routes and of expected failures. Here, penalties for failures correspond to return trips to the depot. The vehicle first returns to the depot to unload, then resumes its trip as originally planned. This article studies an implementation of the Integer L-shaped method for the exact solution of the SVRP. It develops new lower bounds on the expected penalty for failures. In addition, it provides variants of the optimality cuts for the SVRP that also hold at fractional solutions. Numerical experiments indicate that some instances involving up to 100 customers and few vehicles can be solved to optimality within a relatively short computing time.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 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".