Online algorithms for the multi-vehicle inventory-routing problem with real-time demands
Bibliographic record
Abstract
The increasing availability of sophisticated information and communication technology has stimulated new research within the distribution logistics area in the last few decades. Real-time information is crucial to ensure not only the competitiveness of a company but also its survival in the e-commerce era. Companies try to offer delivery to their customers within a few hours of receiving a request. In addition, real-time information can be exploited in systems that operate under emergencies, where response time is critical. We model and solve a multi-vehicle inventory-routing problem in which new service requests are revealed dynamically over time, in real-time or online. For this problem, we propose a class of online algorithms based on iteratively solving integer programming models. These models are solved through a tailored branch-and-cut method, in which several families of valid inequalities are separated and dynamically introduced in the model or through a matheuristic to speed up the solution process. We carry out a competitive analysis that allows us to prove the competitive ratio of the online algorithms we propose and, therefore, to evaluate their performance with respect to the optimal solution of the offline problem, in the worst case. An extensive computational experience on benchmark instances shows that these algorithms are also effective on average and require short computational time when the matheuristic is applied to solve the integer programming models. Additional tests on large real-world instances indicate that the proposed solution methods achieve performance that remains reasonable for the size of these instances. • We study the multi-vehicle inventory-routing problem with real-time demands. • We propose a class of online algorithms for this problem. • A theoretical competitive analysis provides performance guarantees of the algorithms. • An extensive computational study complements the theoretical analysis. • Empirical performance is better than the theoretical competitive ratios.
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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 | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.003 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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".