An Inventory-Routing Problem with Pickups and Deliveries Arising in the Replenishment of Automated Teller Machines
Bibliographic record
Abstract
The purpose of this paper is to introduce, model, and solve a rich multiperiod inventory-routing problem with pickups and deliveries motivated by the replenishment of automated teller machines in the Netherlands. Commodities can be brought to and from the depot, as well as being exchanged among customers to efficiently manage their inventory shortages and surpluses. A single customer can both provide and receive commodities at different periods, since its demand changes dynamically throughout the planning horizon and can be either positive or negative. In the case study, new technology provides these machines with the additional functionality of receiving deposits and reissuing banknotes to subsequent customers. We first formulate the problem as a very large-scale mixed-integer linear programming model. Given the size and complexity of the problem, we first decompose it into several more manageable subproblems by means of a clustering procedure, and we further simplify the subproblems by fixing some variables. The resulting subproblems are strengthened through the generation of valid inequalities and solved by branch and cut. We assess the performance of the proposed solution methodology through extensive computational experiments using real data. The results show that we are able to obtain good lower and upper bounds for this new and challenging practical problem.
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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 | 0.003 |
| 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 | 0.004 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".