Two-echelon prize-collecting vehicle routing with time windows and vehicle synchronization: A branch-and-price approach
Bibliographic record
Abstract
The steady growth in e-commerce and grocery deliveries within cities strains the available infrastructure in urban areas by increasing freight movements, aggravating traffic congestion, and air and noise pollution. This research introduces the Two-Echelon Prize-Collecting Vehicle Routing Problem with Time Windows and Vehicle Synchronization , where deliveries are carried out by smaller low- or zero-emission vehicles and larger trucks. Given their capacity restrictions, the smaller vehicles can only deliver small-sized orders and must be replenished via depot locations or larger-sized trucks. Besides replenishing smaller vehicles at satellite locations, larger trucks can deliver small orders and larger items. Managing these two types of fleets in an urban setting under consideration of capacity limitations, tight delivery time windows, vehicle synchronization, and selective order fulfillment is challenging. We model this problem on a time-expanded network and apply network reduction by considering the time window constraints. In addition, we propose a branch-and-price algorithm capable of solving instances with up to 200 customers, which continuously outperforms a state-of-the-art general-purpose optimization solver. Moreover, we present several managerial insights concerning synchronization, vehicles, and the placement of depot/satellite locations. • We address a novel last-mile distribution problem with vehicle synchronization. • Selective order fulfillment, multiple trips, and tight and long time windows are integrated into a two-echelon setting. • A branch-and-price algorithm is proposed to solve the problem for different-sized instances. • Results show that our method finds optimal solutions for instances with up to 200 customers. • We derive detailed managerial insights by studying the effects of synchronization and different instance structures.
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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 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.008 | 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".