---
title: "Vehicle routing problem: formula, variables and example"
description: "Vehicle routing problem explained: variables, a worked example, related methods and assumptions. Plans the cheapest routes for a fleet of capacity Q to serve every customer once."
url: https://scholar4ai.com/equations/vehicle-routing-problem
markdown_url: https://scholar4ai.com/equations/vehicle-routing-problem.md
license: CC BY-NC 4.0 (https://creativecommons.org/licenses/by-nc/4.0/)
share_text: "Vehicle routing problem explained: variables, a worked example, related methods and assumptions. Plans the cheapest routes for a fleet of capacity Q to serve every customer once. (as of 2026-11-05)"
data_url: https://scholar4ai.com/data/rankings.json
updated: 2026-11-05T06:02:37+09:00
window: 2026-10-07 to 2026-11-05
source: OpenAlex (CC0)
---

# Vehicle routing problem

$$
\min \sum_{(i,j)} c_{ij}\, x_{ij}\quad \text{s.t.}\ \sum_{j} x_{ij} = 1\ \ \forall i,\quad \sum_{i \in r} d_i \le Q
$$

Plans the cheapest routes for a fleet of capacity Q to serve every customer once.

- area: Optimization and metaheuristics
- 5 papers in the last 7 days
- Names searched for: vehicle routing problem, vehicle routing, VRP

Back to the ranking: https://scholar4ai.com/rankings/equations.md

## 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

- [The Truck Dispatching Problem](https://doi.org/10.1287/mnsc.6.1.80)

Examples use illustrative inputs, not observed research results. Logarithms are natural unless stated otherwise. Guide updated 2026-11-05. Prepared by Scholar4AI. [Editorial and verification policy](/editorial-policy).

## 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

*Papers mentioning it by publication month, Nov 2023 to Oct 2026 (titles, abstracts and keywords; the full texts of earlier months are still being searched)*

| Trend | Nov 23–Oct 24 | Nov 24–Oct 25 | Nov 25–Oct 26 | 36 months |
|---|---:|---:|---:|---:|
|  | 510 | 534 | 590 | 1,634 |

## Papers per year

*Papers per publication year and category*

| Category | 2017 | 2018 | 2019 | 2020 | 2021 | 2022 | 2023 | 2024 | 2025 | 2026 (so far) |
|---|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|
| [Operations Research](https://scholar4ai.com/categories/operations-research.md) | 163 | 154 | 162 | 193 | 202 | 205 | 231 | 434 | 406 | 416 |
| [AI](https://scholar4ai.com/categories/ai.md) | 9 | 26 | 27 | 32 | 35 | 59 | 59 | 94 | 93 | 80 |
| [Information Systems](https://scholar4ai.com/categories/information-systems.md) | 2 | 0 | 3 | 1 | 3 | 1 | 1 | 7 | 2 | 4 |
| [Economics](https://scholar4ai.com/categories/economics.md) | 1 | 3 | 1 | 2 | 0 | 3 | 0 | 2 | 5 | 4 |
| [Management](https://scholar4ai.com/categories/management.md) | 0 | 1 | 3 | 0 | 0 | 1 | 4 | 3 | 3 | 4 |
| [Marketing](https://scholar4ai.com/categories/marketing.md) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 2 |
| [Finance](https://scholar4ai.com/categories/finance.md) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 |
| [Statistics](https://scholar4ai.com/categories/statistics.md) | 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

*Journals with the most papers, since 2023*

| # | Journal | Papers |
|---:|---|---:|
| 1 | [Computers & Operations Research](https://scholar4ai.com/journals/computers-operations-research.md) | 205 |
| 2 | [European Journal of Operational Research](https://scholar4ai.com/journals/european-journal-of-operational-research.md) | 202 |
| 3 | [Transportation Research Part E Logistics and Transportation Review](https://scholar4ai.com/journals/transportation-research-part-e-logistics-and-transportation-review.md) | 189 |
| 4 | [Transportation Research Part C Emerging Technologies](https://scholar4ai.com/journals/transportation-research-part-c-emerging-technologies.md) | 134 |
| 5 | [Computers & Industrial Engineering](https://scholar4ai.com/journals/computers-industrial-engineering.md) | 133 |
| 6 | [Expert Systems with Applications](https://scholar4ai.com/journals/expert-systems-with-applications.md) | 131 |
| 7 | [Annals of Operations Research](https://scholar4ai.com/journals/annals-of-operations-research.md) | 114 |
| 8 | [Transportation Research Part B Methodological](https://scholar4ai.com/journals/transportation-research-part-b-methodological.md) | 47 |
| 9 | [OR Spectrum](https://scholar4ai.com/journals/or-spectrum.md) | 39 |
| 10 | [Swarm and Evolutionary Computation](https://scholar4ai.com/journals/swarm-and-evolutionary-computation.md) | 31 |

*Institutions with the most papers, since 2023*

| # | Institution | Papers |
|---:|---|---:|
| 1 | [Hong Kong Polytechnic University](https://scholar4ai.com/institutions/hong-kong-polytechnic-university.md) | 59 |
| 2 | [Eindhoven University of Technology](https://scholar4ai.com/institutions/eindhoven-university-of-technology.md) | 50 |
| 3 | [Centre National de la Recherche Scientifique](https://scholar4ai.com/institutions/centre-national-de-la-recherche-scientifique.md) | 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](https://scholar4ai.com/institutions/delft-university-of-technology.md) | 34 |
| 7 | [Beijing Jiaotong University](https://scholar4ai.com/institutions/beijing-jiaotong-university.md) | 33 |
| 8 | [Southwest Jiaotong University](https://scholar4ai.com/institutions/southwest-jiaotong-university.md) | 31 |
| 9 | [Beihang University](https://scholar4ai.com/institutions/beihang-university.md) | 25 |
| 10 | Polytechnique Montréal | 25 |

*Countries with the most papers, since 2023*

| # | 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 |

*Keywords with the most papers, since 2023*

| # | Keyword | Papers |
|---:|---|---:|
| 1 | [vehicle routing](https://scholar4ai.com/keywords/vehicle-routing.md) | 600 |
| 2 | time windows | 190 |
| 3 | [mixed-integer linear programming](https://scholar4ai.com/keywords/mixed-integer-linear-programming.md) | 181 |
| 4 | last-mile delivery | 179 |
| 5 | adaptive large neighborhood search | 148 |
| 6 | [combinatorial optimization](https://scholar4ai.com/keywords/combinatorial-optimization.md) | 116 |
| 7 | [metaheuristic optimization](https://scholar4ai.com/keywords/metaheuristic-optimization.md) | 107 |
| 8 | [multi-objective optimization](https://scholar4ai.com/keywords/multi-objective-optimization.md) | 101 |
| 9 | [mixed integer programming](https://scholar4ai.com/keywords/mixed-integer-programming.md) | 92 |
| 10 | capacitated vehicle routing problem | 74 |

## Most-cited papers

*Most-cited papers since 2017*

| # | Citations | Per month | Title | Journal | Published | Authors |
|---:|---:|---:|---|---|---|---|
| 1 | 745 | 9.7 | [A Coevolutionary Framework for Constrained Multiobjective Optimization Problems](https://doi.org/10.1109/tevc.2020.3004012) | [IEEE Transactions on Evolutionary Computation](https://scholar4ai.com/journals/ieee-transactions-on-evolutionary-computation.md) | 2020-06-22 | Ye Tian, Tao Zhang, Jianhua Xiao et al. |
| 2 | 637 | 5.5 | [The electric vehicle routing problem with nonlinear charging function](https://doi.org/10.1016/j.trb.2017.02.004) | [Transportation Research Part B Methodological](https://scholar4ai.com/journals/transportation-research-part-b-methodological.md) | 2017-03-01 | Alejandro Montoya, Christelle Guéret, Jorge E. Mendoza et al. |
| 3 | 627 | 5.9 | [On the min-cost Traveling Salesman Problem with Drone](https://doi.org/10.1016/j.trc.2017.11.015) | [Transportation Research Part C Emerging Technologies](https://scholar4ai.com/journals/transportation-research-part-c-emerging-technologies.md) | 2017-12-22 | Quang Minh Ha, Yves Deville, Quang Dung Pham et al. |
| 4 | 573 | 6.3 | [An adaptive large neighborhood search metaheuristic for the vehicle routing problem with drones](https://doi.org/10.1016/j.trc.2019.02.018) | [Transportation Research Part C Emerging Technologies](https://scholar4ai.com/journals/transportation-research-part-c-emerging-technologies.md) | 2019-03-22 | David Sacramento, David Pisinger, Stefan Røpke |
| 5 | 560 | 6.1 | [Vehicle routing problem with drones](https://doi.org/10.1016/j.trb.2019.03.005) | [Transportation Research Part B Methodological](https://scholar4ai.com/journals/transportation-research-part-b-methodological.md) | 2019-03-13 | Zheng Wang, Jiuh‐Biing Sheu |
| 6 | 505 | 4.8 | [A survey of dial-a-ride problems: Literature review and recent developments](https://doi.org/10.1016/j.trb.2018.02.001) | [Transportation Research Part B Methodological](https://scholar4ai.com/journals/transportation-research-part-b-methodological.md) | 2018-02-14 | Sin C. Ho, Wai Yuen Szeto, Yong‐Hong Kuo et al. |
| 7 | 391 | 6.3 | [The electric vehicle routing problem and its variations: A literature review](https://doi.org/10.1016/j.cie.2021.107650) | [Computers & Industrial Engineering](https://scholar4ai.com/journals/computers-industrial-engineering.md) | 2021-08-30 | İlker Küçükoğlu, Reginald Dewil, Dirk Cattrysse |
| 8 | 352 | 5.2 | [Learning Improvement Heuristics for Solving Routing Problems](https://doi.org/10.1109/tnnls.2021.3068828) | [IEEE Transactions on Neural Networks and Learning Systems](https://scholar4ai.com/journals/ieee-transactions-on-neural-networks-and-learning-systems.md) | 2021-04-01 | Yaoxin Wu, Wen Wu Song, Zhiguang Cao et al. |
| 9 | 346 | 2.9 | [The electric location routing problem with time windows and partial recharging](https://doi.org/10.1016/j.ejor.2017.01.011) | [European Journal of Operational Research](https://scholar4ai.com/journals/european-journal-of-operational-research.md) | 2017-01-10 | Maximilian Schiffer, Grit Walther |
| 10 | 345 | 3.7 | [Truck-drone hybrid delivery routing: Payload-energy dependency and No-Fly zones](https://doi.org/10.1016/j.ijpe.2019.01.010) | [International Journal of Production Economics](https://scholar4ai.com/journals/international-journal-of-production-economics.md) | 2019-01-09 | Ho Young Jeong, Byung Duk Song, Seokcheon Lee |

Archive counts by publication year: a paper counts when its title, abstract or keywords name the equation, or when OpenAlex's full-text search finds it there (searched for the last 30 days' papers and, by a pass over the past years, for older ones). Names added to the list later are looked for in older papers as the archive is read again.

*Papers mentioning Vehicle routing problem, newest first.*

| Date | Title | Journal | Authors | Affiliations |
|---|---|---|---|---|
| 2026-11-02 | [Rural passenger-freight demand-responsive transit with reconfigurable vehicle capacity and 3D loading constraints](https://doi.org/10.1016/j.tre.2026.105345) | [Transportation Research Part E Logistics and Transportation Review](https://scholar4ai.com/journals/transportation-research-part-e-logistics-and-transportation-review.md) | Jiabin Wang, 孙启鹏, Zhen Shang et al. | Chang'an University; University College Dublin; University of Belgrade |
| 2026-10-31 | [Collaborative routing and cost allocation for urban logistics alliances with interdepot transfers](https://doi.org/10.1016/j.tranpol.2026.104514) | [Transport Policy](https://scholar4ai.com/journals/transport-policy.md) | Jianbin Li, Zhisheng Wang, Mengcheng Guan et al. | Huazhong University of Science and Technology; University of Michigan–Dearborn; Wuhan University |
| 2026-10-31 | [Theoretical lower bounds for a parallel batch scheduling problem](https://doi.org/10.1007/s10951-026-00887-y) | [Journal of Scheduling](https://scholar4ai.com/journals/journal-of-scheduling.md) | Marie-Louise Lackner, Francesca Da Ros, Nysret Musliu | TU Wien; University of Udine |
| 2026-10-30 | [Chance constrained optimization of hub transport systems](https://doi.org/10.1016/j.cor.2026.107709) | [Computers & Operations Research](https://scholar4ai.com/journals/computers-operations-research.md) | Max Bourgeat, Öykü Naz Attila, Rémy Chevrier et al. | Centre interuniversitaire de recherche sur les réseaux d'entreprise, la logistique et le transport; Polytechnique Montréal; Société Nationale des Chemins de Fer Français (France); … |
| 2026-10-30 | [Energy-Aware Aerial-Ground collaborative routing for simultaneous pickup and delivery](https://doi.org/10.1016/j.eswa.2026.134822) | [Expert Systems with Applications](https://scholar4ai.com/journals/expert-systems-with-applications.md) | Jingfeng Guo, Rui Song, 何世伟 | Beijing Jiaotong University |
| 2026-10-29 | [A simulation-driven approach to last-mile logistics analysis considering microlevel operational sequences for efficient delivery planning](https://doi.org/10.1007/s10479-026-07429-x) | [Annals of Operations Research](https://scholar4ai.com/journals/annals-of-operations-research.md) | Shamimur Rahman, Dana Zamorano, Tzu‐Liang Bill Tseng et al. | The University of Texas at El Paso; North Carolina State University |
| 2026-10-28 | [Centralized truck platooning matching with compliance considerations](https://doi.org/10.1016/j.trb.2026.103628) | [Transportation Research Part B Methodological](https://scholar4ai.com/journals/transportation-research-part-b-methodological.md) | Pooria Choobchian, Bo Zou, Limon Barua | University of Illinois Chicago; Argonne National Laboratory |
| 2026-10-27 | [A Pareto archive-driven hyper-heuristic for multi-objective cross-regional agricultural machinery scheduling](https://doi.org/10.1016/j.eswa.2026.134760) | [Expert Systems with Applications](https://scholar4ai.com/journals/expert-systems-with-applications.md) | Wenkang Zhang, Longzhe Quan, Jian Chu | Anhui Agricultural University; Hefei University of Technology |
| 2026-10-27 | [A Q-learning enhanced multi-objective memetic algorithm for vehicle routing with simultaneous pickup-delivery and time windows](https://doi.org/10.1016/j.swevo.2026.102582) | [Swarm and Evolutionary Computation](https://scholar4ai.com/journals/swarm-and-evolutionary-computation.md) | 赖雪瑜, Yalan Zhou | Guangdong University Of Finances and Economics; Guangdong University of Finance |
| 2026-10-24 | [Timebox-enhanced evolutionary algorithm for electric vehicle–drone routing problem with drone stations and time windows](https://doi.org/10.1016/j.swevo.2026.102580) | [Swarm and Evolutionary Computation](https://scholar4ai.com/journals/swarm-and-evolutionary-computation.md) | Setyo Tri Windras Mara, Ruhul Amin Sarker, Saber Mohammed Elsayed et al. | UNSW Canberra; University of Sharjah; Basque Center for Applied Mathematics; … |
| 2026-10-24 | [Routing decisions, human judgement, and digitalisation in high-friction logistics environments](https://doi.org/10.1016/j.rtbm.2026.101921) | [Research in Transportation Business & Management](https://scholar4ai.com/journals/research-in-transportation-business-management.md) | Dilay Çelebi, Ena Cekic | South East European Research Centre; University of York |
| 2026-10-23 | [A matheuristic method for a time-dependent heterogeneous vehicle routing problem with delivery options](https://doi.org/10.1016/j.trb.2026.103623) | [Transportation Research Part B Methodological](https://scholar4ai.com/journals/transportation-research-part-b-methodological.md) | Youxuan Pan, Jingyi Zhao, Haoxiang Yang et al. | Southwestern University of Finance and Economics; Vienna University of Economics and Business; Shenzhen Research Institute of Big Data; … |
| 2026-10-23 | [Learning Dominant States in Elementary Resource Constrained Shortest Path Problems](https://doi.org/10.1007/s10479-026-07457-7) | [Annals of Operations Research](https://scholar4ai.com/journals/annals-of-operations-research.md) | Saverio Basso, Alessandro Minoli, Matteo Salani | University of Applied Sciences and Arts of Southern Switzerland; Dalle Molle Institute for Artificial Intelligence Research |
| 2026-10-20 | [A carbon-sensitive heterogeneous fleet framework for time-critical urban quick-commerce delivery with synchronised drone integration](https://doi.org/10.1016/j.rtbm.2026.101919) | [Research in Transportation Business & Management](https://scholar4ai.com/journals/research-in-transportation-business-management.md) | Gülseli İşler, Harun Reşit Yazg̈an, Muhammed Sever | Sakarya University |
| 2026-10-20 | [A new hierarchical matheuristic applied to the helicopter routing problems (HRP)](https://doi.org/10.1007/s10732-026-09609-1) | [Journal of Heuristics](https://scholar4ai.com/journals/journal-of-heuristics.md) | André Machado, Rodrigo Rosa, Hendrigo Venes et al. | Universidade Federal do Espírito Santo |
| 2026-10-19 | [Exact and heuristic approaches for the multi-vehicle covering tour problem with prize collecting](https://doi.org/10.1016/j.eswa.2026.134810) | [Expert Systems with Applications](https://scholar4ai.com/journals/expert-systems-with-applications.md) | Modoukpè Maryse Eudoxie ASSANVI, Marcos Costa Roboredo | Universidade Federal Fluminense |
| 2026-10-19 | [Coherent local explanations for mathematical optimization](https://doi.org/10.1016/j.orl.2026.107549) | [Operations Research Letters](https://scholar4ai.com/journals/operations-research-letters.md) | Daan Otto, Jannis Kurtz, Ş. İlker Birbil | University of Amsterdam |
| 2026-10-18 | [Two-Echelon Electric Vehicle Routing with Mobile Parcel Lockers: A Three-Stage Adaptive Matheuristic with Exact Replenishment](https://doi.org/10.1016/j.cor.2026.107706) | [Computers & Operations Research](https://scholar4ai.com/journals/computers-operations-research.md) | Nima Moradi, Fereshteh Mafakheri, Chun Wang | Concordia University; Université du Québec à Montréal; École Nationale d'Administration Publique |
| 2026-10-16 | [A mixed-integer linear programming approach to container terminal layout optimization: application to the port of Piraeus](https://doi.org/10.1007/s12351-026-01103-7) | [Operational Research](https://scholar4ai.com/journals/operational-research.md) | Konstantinos Charalampidis, Ιωάννης Καμπούρης, Tatiana P. Moschovou | National Technical University of Athens |
| 2026-10-16 | [A decomposable branch-and-price formulation for optimal classification trees](https://doi.org/10.1007/s12532-026-00343-0) | [Mathematical Programming Computation](https://scholar4ai.com/journals/mathematical-programming-computation.md) | Elif Rana Yöner, Taghi Khaniyev, Özlem Karsu | Bilkent University |
| 2026-10-16 | [A hybrid metaheuristic for the family capacitated vehicle routing problem](https://doi.org/10.1007/s10732-026-09607-3) | [Journal of Heuristics](https://scholar4ai.com/journals/journal-of-heuristics.md) | Bruno Oliveira, D閎ora Balduci Lima, Marcos Costa Roboredo | Universidade Federal Fluminense |
| 2026-10-16 | [Transit-MP: Transit-prioritized max-pressure control in sparse connected vehicle environments](https://doi.org/10.1016/j.trb.2026.103622) | [Transportation Research Part B Methodological](https://scholar4ai.com/journals/transportation-research-part-b-methodological.md) | Chaopeng Tan, Hao Liu, Dingshan Sun et al. | Technische Universität Dresden; Delft University of Technology; University of Maine; … |
| 2026-10-15 | [Operations optimization in multi-modal relay-based delivery systems: Plan-based model and nested exact algorithm](https://doi.org/10.1016/j.trb.2026.103618) | [Transportation Research Part B Methodological](https://scholar4ai.com/journals/transportation-research-part-b-methodological.md) | Xueting He, Lu Zhen, Shuaian Wang et al. | Shanghai University; Hong Kong Polytechnic University; HEC Montréal; … |
| 2026-10-15 | [Last-mile delivery with multiple deliverypersons: Formulation and exact solution methods for a two-echelon location-routing problem](https://doi.org/10.1016/j.trc.2026.106069) | [Transportation Research Part C Emerging Technologies](https://scholar4ai.com/journals/transportation-research-part-c-emerging-technologies.md) | Fernando Ribeiro de Senna, Leandro Callegari Coelho, Reinaldo Morábito et al. | Universidade Federal de São Carlos; Université Laval; Centre interuniversitaire de recherche sur les réseaux d'entreprise, la logistique et le transport |
| 2026-10-15 | [Metropolis-scale resilient and trustworthy traffic flow inference using multi-source data](https://doi.org/10.1016/j.trc.2026.106083) | [Transportation Research Part C Emerging Technologies](https://scholar4ai.com/journals/transportation-research-part-c-emerging-technologies.md) | Qishen Zhou, Yifan Zhang, Michail Makridis et al. | Jilin University; City University of Hong Kong; City University of Hong Kong (Dongguan); … |
| 2026-10-14 | [Study of robust features in formulating guidance for heuristic algorithms for solving the vehicle routing problem](https://doi.org/10.1007/s10732-026-09603-7) | [Journal of Heuristics](https://scholar4ai.com/journals/journal-of-heuristics.md) | Bachtiar Herdianto, Romain Billot, Flavien Lucas et al. | Institut national de recherche en sciences et technologies du numérique; Institut National des Sciences Appliquées de Lyon; Centre National de la Recherche Scientifique; … |
| 2026-10-13 | [Dynamic mobile production vehicle routing problem](https://doi.org/10.1016/j.cie.2026.112446) | [Computers & Industrial Engineering](https://scholar4ai.com/journals/computers-industrial-engineering.md) | Min Wen, Yue Wang, Stefan Røpke | Xi’an Jiaotong-Liverpool University; Huazhong University of Science and Technology; Technical University of Denmark |
| 2026-10-13 | [Hierarchical facility location-inventory-routing problem for maximal joint and gradual coverage](https://doi.org/10.1007/s12351-026-01095-4) | [Operational Research](https://scholar4ai.com/journals/operational-research.md) | Büşra Sultan Bayat, Ertan Yakıcı, Levent Erişkin et al. | Milli Savunma Üniversitesi; Çankaya University; Piri Reis University; … |
| 2026-10-12 | [A sector-based sparse variable competition framework for large-scale many-objective optimization](https://doi.org/10.1016/j.eswa.2026.134638) | [Expert Systems with Applications](https://scholar4ai.com/journals/expert-systems-with-applications.md) | Qingxia Shang, Xinman Zhao, Bin Qian et al. | Kunming University of Science and Technology; Chongqing University |
| 2026-10-10 | [Toward smart wildfire surveillance: Multi-depot drone routing optimization using bio-inspired algorithms](https://doi.org/10.1016/j.cie.2026.112441) | [Computers & Industrial Engineering](https://scholar4ai.com/journals/computers-industrial-engineering.md) | Mohamed Salim Amri Sakhri | IMT Mines Albi; Centre de Génie Industriel |
| 2026-10-10 | [Optimal driving assignment strategies for plug-in hybrid electric heavy duty trucks](https://doi.org/10.1016/j.clscn.2026.100379) | [Cleaner Logistics and Supply Chain](https://scholar4ai.com/journals/cleaner-logistics-and-supply-chain.md) | Javier Jareño, Bernabè Dorronsoro, P. Ruiz | Universidad de Cádiz |
| 2026-10-09 | [Rolling-horizon replanning for two-echelon truck–drone routing with dynamically released pickups](https://doi.org/10.1016/j.trc.2026.106067) | [Transportation Research Part C Emerging Technologies](https://scholar4ai.com/journals/transportation-research-part-c-emerging-technologies.md) | Fan Yu, Yanzhan Chen, Qun Chen et al. | Central South University |
| 2026-10-09 | [Schedules for pick-and-place robots](https://doi.org/10.1007/s10951-026-00888-x) | [Journal of Scheduling](https://scholar4ai.com/journals/journal-of-scheduling.md) | Peter Buchholz, Alexander Puzicha | TU Dortmund University |
| 2026-10-09 | [Infrastructure-based autonomous mobile robots for internal logistics — challenges and future perspectives](https://doi.org/10.1016/j.robot.2026.105798) | [Robotics and Autonomous Systems](https://scholar4ai.com/journals/robotics-and-autonomous-systems.md) | Erik Brorsson, Kristian Ceder, Ze Zhang et al. | Volvo (Sweden); Chalmers University of Technology; Chalmers Industriteknik; … |
| 2026-10-08 | [Dynamic ridesharing matching and vehicle routing optimization of app-based taxis](https://doi.org/10.1016/j.trc.2026.106049) | [Transportation Research Part C Emerging Technologies](https://scholar4ai.com/journals/transportation-research-part-c-emerging-technologies.md) | Xiqiong Chen, Rufang Pan, Xun Zhou et al. | Chang'an University |
| 2026-10-07 | [From fleet to crowd: A discussion on challenges in implementing crowdsourced last mile delivery in the express courier market using adaptive BMI theory](https://doi.org/10.1016/j.clrc.2026.100506) | [Cleaner and Responsible Consumption](https://scholar4ai.com/journals/cleaner-and-responsible-consumption.md) | Nipuni Piyasena, Ferry Jie, Violetta Wilk et al. | Edith Cowan University |
| 2026-10-07 | [Q-learning based large neighborhood search with load-aware destroy for load-dependent multi depot heterogeneous fleet vehicle routing problem](https://doi.org/10.1016/j.cie.2026.112420) | [Computers & Industrial Engineering](https://scholar4ai.com/journals/computers-industrial-engineering.md) | Xinyi Wu, Shengguang Xiong, Jiaqing Li et al. | Wuhan University of Technology; University College London |
| 2026-10-07 | [Using Kernel Density Estimation and Density Clustering to Simplify Vehicle Routing Optimization in Urban Last-Mile Logistics](https://doi.org/10.1007/s40745-026-00732-1) | [Annals of Data Science](https://scholar4ai.com/journals/annals-of-data-science.md) | Weslley Moura, António Grilo, Paulo Nováis | University of Minho; Universidade Nova de Lisboa |
| 2026-10-07 | [Pessimistic bilevel optimization approach for decision–focused learning](https://doi.org/10.1007/s12532-026-00344-z) | [Mathematical Programming Computation](https://scholar4ai.com/journals/mathematical-programming-computation.md) | Diego Jiménez, Bernardo K. Pagnoncelli, Hande Yaman | SKEMA Business School; Université Côte d'Azur; KU Leuven |

## 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

```bibtex
@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}
}
```

License: CC BY-NC 4.0 (https://creativecommons.org/licenses/by-nc/4.0/).