Integrated and sequential algorithms for the robust two-echelon location-routing problem under demand uncertainty
Bibliographic record
Abstract
This paper addresses the two-echelon capacitated location-routing problem (2E-CLRP) when faced with demand uncertainty. We assume that the customer’s demands at the second echelon are uncertain and design a two-echelon distribution network where open satellites, served from a single depot, have sufficient capacities to handle the variation in demand. At the same time, the planned routes must remain feasible for all values of demand within an uncertainty set. We propose a robust counterpart for an integrated model of the 2E-CLRP and solve it using an adaptive large neighborhood search heuristic and a branch-and-cut algorithm. We also design four non-integrated solution approaches based on the robust counterparts for the 2E-CLRP subproblems, including the vehicle routing problem (VRP), the facility location problem (FLP), the location-routing problem (LRP), and the two-echelon FLP (2E-FLP). The importance of an integrated approach to 2E-CLRP is demonstrated by comparing it to non-integrated approaches. Results show that early integration of location and routing decisions leads to better location and total costs. We also evaluate the price of robustness and the trade-off between conservative and riskier robust solutions using a Monte Carlo simulation. We perform a series of computational experiments to validate the proposed algorithms using benchmark instances for the deterministic 2E-CLRP, LRP and robust VRP.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".