The workforce scheduling and routing problem with park‐and‐loop
Bibliographic record
Abstract
Abstract This article introduces formulations and an exact algorithm for the workforce scheduling and routing problem with park‐and‐loop. This problem extends the standard workforce scheduling and routing problem by allowing the use of walking subtours in the routes. We introduce a compact arc‐based formulation as well as a path‐based formulation with an exponential number of variables. To efficiently solve the latter, we propose a branch‐price‐and‐cut algorithm that leverages state‐of‐the‐art techniques, including a tailored version of the pulse algorithm to solve the pricing problem and the separation of subset row inequalities to strengthen the lower bound. We report on computational experiments carried out on a set of instances with up to 75 tasks adapted from the literature. The results show that our method systematically outperforms a standard MIP solver, proving optimality for 241 out of 324 instances. We also report experiments on the closely‐related service technician routing and scheduling problem, where our method delivered 12 new best solutions on a 54‐instance testbed from the literature.
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 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.007 | 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 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".