Mathematical programming models for order picking in warehouses with decoupling of picker and cart
Bibliographic record
Abstract
As a special Travelling Salesman Problem (TSP), the Single-Picker Routing Problem (SPRP) in warehouses is of important theoretical and practical significance. In manual order picking, the items are usually picked up by a picker with a cart. To speed up the picking process, the picker is allowed to stop the cart to pick up the items individually and return to the location of the cart. This paper proposes a mixed integer linear programming formulation for an order picking problem with the decoupling of the picker and the cart in a multi-block warehouse, where the picker capacity is at most four. And based on this model, order batching problem is also analysed. Through numerical experiments, the cost of above decoupling problems is computed under different settings of the speed ratio and the capacity of the picker while he/she is travelling alone. The results indicate how the decoupling of picker and cart leads to cost reduction. Our model shows good performance for orders of small and medium scale and hence has great potential to improve the order picking operation which is executed by decoupling containers and robots/vehicles in modern digital warehouse systems.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.003 |
| 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".