Vehicle routing problem
← Most-used equations and models · All optimization and metaheuristics equations
Plans the cheapest routes for a fleet of capacity Q to serve every customer once.
LaTeX: \min \sum_{(i,j)} c_{ij}\, x_{ij}\quad \text{s.t.}\ \sum_{j} x_{ij} = 1\ \ \forall i,\quad \sum_{i \in r} d_i \le Q
Variables and notation#
c_ij is travel cost, x_ij a binary arc-use decision, d_i customer demand, r a route and Q vehicle capacity.
Worked example#
A candidate route depot→A→B→depot with leg costs 2,3,4 costs 9. Demands 2 and 3 fit capacity 5 since 2+3≤5.
Related methods and when to use them#
VRP adds vehicle capacity and multiple routes to traveling-salesperson routing. The displayed constraints are abbreviated: depot rules, flow balance, route consistency and subtour elimination are also needed for a complete model.
Sources and further reading#
Key findings#
- Vehicle routing problem was mentioned in 39 papers in the last 30 days (2026-10-07 to 2026-11-05), ranking #34 of the 248 equations and models mentioned.
- By journal category: Operations Research (29), AI (7), Economics (1), Marketing (1) and Statistics (1).
- Most of them appeared in Expert Systems with Applications (4), Transportation Research Part B Methodological (4) and Transportation Research Part C Emerging Technologies (4).
- Often mentioned together with Linear and integer programming (18), Genetic algorithm (10) and Simulated annealing (6).
- Datasets named in the same papers: OpenStreetMap (3), Eurostat (1) and Thomson Reuters 13F holdings (1).
- From Nov 2023 to Oct 2026, 1,634 archived papers mentioned Vehicle routing problem in their title, abstract or keywords (the search of earlier months' full texts is still under way), most of them in Sep 2026 (71).
- From 2017 to 2026 (so far), Vehicle routing problem was mentioned in 3,151 papers in the tracked journals, most of them in operations research (2,566), AI (514) and information systems (24).
- 511 of them were published in 2025, against 175 in 2017.
- Since 2023, the institutions with the most of these papers were Hong Kong Polytechnic University (59), Eindhoven University of Technology (50) and Centre National de la Recherche Scientifique (49).
- The journals publishing most of them were Computers & Operations Research (205), European Journal of Operational Research (202) and Transportation Research Part E Logistics and Transportation Review (189).
- The most-cited of them is “A Coevolutionary Framework for Constrained Multiobjective Optimization Problems” (IEEE Transactions on Evolutionary Computation, 2020), with 745 citations.
Mentions over 36 months#
| Trend | Nov 23–Oct 24 | Nov 24–Oct 25 | Nov 25–Oct 26 | 36 months |
|---|---|---|---|---|
| 510 | 534 | 590 | 1,634 |
Papers per year#
20172026 (so far)
| Category | 2017 | 2018 | 2019 | 2020 | 2021 | 2022 | 2023 | 2024 | 2025 | 2026 (so far) |
|---|---|---|---|---|---|---|---|---|---|---|
| Operations Research | 163 | 154 | 162 | 193 | 202 | 205 | 231 | 434 | 406 | 416 |
| AI | 9 | 26 | 27 | 32 | 35 | 59 | 59 | 94 | 93 | 80 |
| Information Systems | 2 | 0 | 3 | 1 | 3 | 1 | 1 | 7 | 2 | 4 |
| Economics | 1 | 3 | 1 | 2 | 0 | 3 | 0 | 2 | 5 | 4 |
| Management | 0 | 1 | 3 | 0 | 0 | 1 | 4 | 3 | 3 | 4 |
| Marketing | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 2 |
| Finance | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 |
| Statistics | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| All categories | 175 | 184 | 197 | 228 | 240 | 269 | 295 | 541 | 511 | 511 |
Where the papers come from#
| # | Journal | Papers |
|---|---|---|
| 1 | Computers & Operations Research | 205 |
| 2 | European Journal of Operational Research | 202 |
| 3 | Transportation Research Part E Logistics and Transportation Review | 189 |
| 4 | Transportation Research Part C Emerging Technologies | 134 |
| 5 | Computers & Industrial Engineering | 133 |
| 6 | Expert Systems with Applications | 131 |
| 7 | Annals of Operations Research | 114 |
| 8 | Transportation Research Part B Methodological | 47 |
| 9 | OR Spectrum | 39 |
| 10 | Swarm and Evolutionary Computation | 31 |
| # | Institution | Papers |
|---|---|---|
| 1 | Hong Kong Polytechnic University | 59 |
| 2 | Eindhoven University of Technology | 50 |
| 3 | Centre National de la Recherche Scientifique | 49 |
| 4 | Centre interuniversitaire de recherche sur les réseaux d'entreprise, la logistique et le transport | 47 |
| 5 | HEC Montréal | 39 |
| 6 | Delft University of Technology | 34 |
| 7 | Beijing Jiaotong University | 33 |
| 8 | Southwest Jiaotong University | 31 |
| 9 | Beihang University | 25 |
| 10 | Polytechnique Montréal | 25 |
| # | Country | Papers |
|---|---|---|
| 1 | China | 552 |
| 2 | United States | 229 |
| 3 | United Kingdom | 181 |
| 4 | Italy | 147 |
| 5 | Germany | 142 |
| 6 | France | 139 |
| 7 | Canada | 135 |
| 8 | Netherlands | 135 |
| 9 | Hong Kong | 91 |
| 10 | Spain | 83 |
| # | Keyword | Papers |
|---|---|---|
| 1 | vehicle routing | 600 |
| 2 | time windows | 190 |
| 3 | mixed-integer linear programming | 181 |
| 4 | last-mile delivery | 179 |
| 5 | adaptive large neighborhood search | 148 |
| 6 | combinatorial optimization | 116 |
| 7 | metaheuristic optimization | 107 |
| 8 | multi-objective optimization | 101 |
| 9 | mixed integer programming | 92 |
| 10 | capacitated vehicle routing problem | 74 |
Most-cited papers#
Cite this page
Scholar4AI. (2026). Vehicle routing problem. Journal and Conference Research Rankings. Retrieved November 5, 2026, from https://scholar4ai.com/equations/vehicle-routing-problem
@misc{scholar4ai-equations-vehicle-routing-problem,
author = {{Scholar4AI}},
title = {Vehicle routing problem},
year = {2026},
howpublished = {\url{https://scholar4ai.com/equations/vehicle-routing-problem}},
urldate = {2026-11-05},
note = {Journal and Conference Research Rankings; data from OpenAlex (CC0); licensed CC BY-NC 4.0}
}