---
title: "Linear and integer programming: formula and papers"
description: "Linear and integer programming was mentioned in 116 papers in the last 30 days (2026-09-27 to 2026-10-26), ranking #4 of the 104 equations and models mentioned."
url: https://scholar4ai.com/equations/linear-and-integer-programming
markdown_url: https://scholar4ai.com/equations/linear-and-integer-programming.md
license: CC BY-NC 4.0 (https://creativecommons.org/licenses/by-nc/4.0/)
share_text: "Linear and integer programming was mentioned in 116 papers in the last 30 days (2026-09-27 to 2026-10-26), ranking #4 of the 104 equations and models mentioned."
data_url: https://scholar4ai.com/data/rankings.json
updated: 2026-10-26T14:32:25+09:00
window: 2026-09-27 to 2026-10-26
source: OpenAlex (CC0)
---

# Linear and integer programming

$$
\min_{x}\ c^\top x\ \ \text{s.t.}\ \ A x \le b,\ x \ge 0,\ x_j \in \mathbb{Z}\ (j \in I)
$$

Optimizes a linear objective under linear constraints, with some variables restricted to integers.

- area: Efficiency and operations
- 7 papers in the last 7 days
- Names searched for: linear programming, linear program, integer programming, integer program, MILP, MINLP, mixed-integer

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

## Key findings

- Linear and integer programming was mentioned in 116 papers in the last 30 days (2026-09-27 to 2026-10-26), ranking #4 of the 104 equations and models mentioned.
- By journal category: Operations Research (100), AI (11), Economics (4) and Finance (1).
- Most of them appeared in European Journal of Operational Research (15), Computers & Industrial Engineering (13) and Transportation Research Part E Logistics and Transportation Review (13).
- Often mentioned together with Logistic regression (logit) (8), Value at risk (VaR) (8) and Expected shortfall (CVaR) (8).
- Datasets named in the same papers: OR-Library (9), Eurostat (3) and International Energy Agency (IEA) (3).
- From Oct 2023 to Sep 2026, 1,944 archived papers mentioned Linear and integer programming in their title, abstract or keywords, most of them in May 2024 (80).

## Mentions over 36 months

*Papers mentioning it by publication month, Oct 2023 to Sep 2026 (titles, abstracts and keywords)*

| Trend | Oct 23–Sep 24 | Oct 24–Sep 25 | Oct 25–Sep 26 | 36 months |
|---|---:|---:|---:|---:|
|  | 789 | 804 | 351 | 1,944 |

*Papers mentioning Linear and integer programming, newest first. Newest 50 of 116 papers; all of them are in /data/papers.json.*

| Date | Title | Journal | Authors | Affiliations |
|---|---|---|---|---|
| 2026-10-24 | [Genetic algorithm based approaches for solving hybrid flowshop scheduling problem under production leveling based lot streaming strategy](https://doi.org/10.1007/s10696-026-09690-5) | [Flexible Services and Manufacturing Journal](https://scholar4ai.com/journals/flexible-services-and-manufacturing-journal.md) | Murat ÇOLAK, Gülşen Aydın Keskin | Kocaeli Üniversitesi; Balıkesir University |
| 2026-10-23 | [Sustainable development goals and waste management in the wheat supply chain under uncertain conditions: implications from an emerging economy](https://doi.org/10.1007/s10479-026-07452-y) | [Annals of Operations Research](https://scholar4ai.com/journals/annals-of-operations-research.md) | Mahsa Rezaee Shirsavar, Misagh Rahbari, Mohammad Mohammadi | Kharazmi University; Islamic Azad University, Tehran; Islamic Azad University, West Tehran Branch |
| 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 | Dalle Molle Institute for Artificial Intelligence Research |
| 2026-10-21 | [Solving two-stage stochastic programming problems using alternating direction method of multipliers](https://doi.org/10.1007/s10589-026-00843-8) | [Computational Optimization and Applications](https://scholar4ai.com/journals/computational-optimization-and-applications.md) | Nouralden Mohammed, Montaz Ali | University of the Witwatersrand |
| 2026-10-21 | [A regional multi-criteria assessment of European education and training systems](https://doi.org/10.1016/j.omega.2026.103683) | [Omega](https://scholar4ai.com/journals/omega.md) | Fernando J. Osório, Luís Cândido Dias | Universidade do Porto; INESC TEC; University of Coimbra |
| 2026-10-20 | [Multi-agent assisted co-evolutionary memetic algorithm for lot-streaming flexible job shop energy-efficient scheduling problem with asynchronous assembly](https://doi.org/10.1016/j.eswa.2026.134552) | [Expert Systems with Applications](https://scholar4ai.com/journals/expert-systems-with-applications.md) | Gan Jiang, Qiuhua Tang, Zikai Zhang et al. | Wuhan University of Science and Technology |
| 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 | [Reusability report: multi-sample omics network inference operates in distinct robustness regimes defined by prior knowledge and data availability](https://doi.org/10.1038/s42256-026-01311-y) | [Nature Machine Intelligence](https://scholar4ai.com/journals/nature-machine-intelligence.md) | Xabier Martinez‐de‐Morentin, Sameer Ahmad Khan, Itziar Cenzano et al. | King Abdullah University of Science and Technology; Ilia State University; Karolinska University Hospital; … |
| 2026-10-19 | [Optimizing product return timing in integrated viable circular manufacturing systems: a two-stage stochastic approach](https://doi.org/10.1007/s10479-026-07450-0) | [Annals of Operations Research](https://scholar4ai.com/journals/annals-of-operations-research.md) | Sobhan Mostafayi Darmian, Fabio Sgarbossa | Norwegian University of Science and Technology |
| 2026-10-19 | [Solutions of two-stage stochastic minimax problems](https://doi.org/10.1007/s10107-026-02428-z) | [Mathematical Programming](https://scholar4ai.com/journals/mathematical-programming.md) | Hailin Sun, Xiaojun Chen | Nanjing Normal University; Hong Kong Polytechnic University |
| 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 |
| 2026-10-18 | [Design of hybrid multi-energy systems under uncertainty: An adjustable robust optimization approach](https://doi.org/10.1016/j.cor.2026.107705) | [Computers & Operations Research](https://scholar4ai.com/journals/computers-operations-research.md) | Patrizia Beraldi, Derya Dinler | University of Calabria; Hacettepe University |
| 2026-10-17 | [Improved approximation algorithm for min-max correlation clustering problem with penalties](https://doi.org/10.1007/s10878-026-01496-3) | [Journal of Combinatorial Optimization](https://scholar4ai.com/journals/journal-of-combinatorial-optimization.md) | Yuebo Huang, Sai Ji, Xiaoyun Tian et al. | Hebei University of Technology; Hainan University; Hoseo University |
| 2026-10-17 | [Modelling phased railway infrastructure upgrades deployment with a case study to ERTMS roll-out](https://doi.org/10.1016/j.trb.2026.103621) | [Transportation Research Part B Methodological](https://scholar4ai.com/journals/transportation-research-part-b-methodological.md) | Paloma Aparecida Freitas Duarte, Lucas P. Veelenturf, Dennis Huisman | Erasmus University Rotterdam; Nederlandse Spoorwegen |
| 2026-10-17 | [A Bayesian-guided aggregation-disaggregation algorithm for transit planning](https://doi.org/10.1016/j.trc.2026.106085) | [Transportation Research Part C Emerging Technologies](https://scholar4ai.com/journals/transportation-research-part-c-emerging-technologies.md) | Golbarg Dokhani, Jisoon Lim, Yiyang Wang et al. | University of Michigan; Amazon (United States) |
| 2026-10-16 | [A Malatya Centrality-based algorithm for optimal solutions to maximum independent set and minimum vertex cover problems in lattice graphs](https://doi.org/10.1007/s12351-026-01126-0) | [Operational Research](https://scholar4ai.com/journals/operational-research.md) | Selman Yakut | Inonu University |
| 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 | [Integrated optimization for fleet sequencing, deploying, and scheduling based on carbon intensity management](https://doi.org/10.1007/s12351-026-01123-3) | [Operational Research](https://scholar4ai.com/journals/operational-research.md) | Jian Du, Yixuan Chen, Ran Zhang et al. | Dalian Jiaotong University |
| 2026-10-16 | [Multi-objective optimization for emergency primary logistics of refined products under pipeline disruption condition: a case study in China](https://doi.org/10.1007/s12351-026-01119-z) | [Operational Research](https://scholar4ai.com/journals/operational-research.md) | Xingyuan Zhou, Mengyun Lyu, Bohong Wang et al. | Beijing Wuzi University; Zhejiang Ocean University; China University of Petroleum, Beijing |
| 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 | [An exact solution algorithm for the bi-level optimization problem of electric vehicles charging station placement](https://doi.org/10.1016/j.trb.2026.103620) | [Transportation Research Part B Methodological](https://scholar4ai.com/journals/transportation-research-part-b-methodological.md) | Mobina Nankali, Michael W. Levin | University of Minnesota |
| 2026-10-16 | [A physical model approach to order lot sizing](https://doi.org/10.1007/s12351-026-01105-5) | [Operational Research](https://scholar4ai.com/journals/operational-research.md) | Tania Daiana Tobares, Margarita Miguelina Mieras, Fabricio Orlando Sanchez Varretti et al. | National Technological University; Instituto de Investigaciones Físicas de Mar del Plata; National University of San Luis |
| 2026-10-15 | [Geopolitical risk spillovers among GCC stock markets, non-renewable energy, and gold: evidence from a quantile connectedness approach](https://doi.org/10.1007/s10258-026-00299-y) | [Portuguese Economic Journal](https://scholar4ai.com/journals/portuguese-economic-journal.md) | Nidhal Mgadmi, Fekria Belhouichet, Ştefan Cristian Gherghina et al. | University of Sfax; Faculty of Economics and Management of Sfax; Bucharest University of Economic Studies; … |
| 2026-10-15 | [Automated optimization modeling and auditing via dual-team multi-LLM-agent cooperative framework](https://doi.org/10.1007/s10489-026-07536-z) | [Applied Intelligence](https://scholar4ai.com/journals/applied-intelligence.md) | Yuan Chiang, Wenhui Fan | Tsinghua University |
| 2026-10-15 | [Interior-Point Methods for Optimal Power Flow with Scheduled Topological Changes under Uncertain Demand](https://doi.org/10.1007/s10479-026-07454-w) | [Annals of Operations Research](https://scholar4ai.com/journals/annals-of-operations-research.md) | S. M. S. Carvalho, Demacio Costa de Oliveira, AURELIO RIBEIRO LEITE OLIVEIRA et al. | Universidade Federal de São Carlos; Universidade Federal Rural de Pernambuco; Universidade Estadual de Campinas (UNICAMP) |
| 2026-10-15 | [Joint fulfillment and consolidation of multi-item orders in e-commerce: A two-phase heuristic](https://doi.org/10.1016/j.cie.2026.112439) | [Computers & Industrial Engineering](https://scholar4ai.com/journals/computers-industrial-engineering.md) | Kehinde G. Ismaila, Adriana Felicia Gabor, Andrei Sleptchenko et al. | Khalifa University of Science and Technology |
| 2026-10-14 | [Modeling and simulating human behavior in large-scale emergency evacuations: A comprehensive review](https://doi.org/10.1016/j.trb.2026.103611) | [Transportation Research Part B Methodological](https://scholar4ai.com/journals/transportation-research-part-b-methodological.md) | Shiva Moslemi, Ada Arıkanoğlu, Vedat Bayram et al. |  |
| 2026-10-13 | [The automated valet parking problem for parking garage service provision](https://doi.org/10.1007/s10951-026-00894-z) | [Journal of Scheduling](https://scholar4ai.com/journals/journal-of-scheduling.md) | Marc Schmidt, Philipp Staudt | Karlsruhe Institute of Technology |
| 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; … |
| 2026-10-13 | [Monte Carlo tree search for the multi-crane scheduling problem with temporal constraints](https://doi.org/10.1007/s10696-026-09691-4) | [Flexible Services and Manufacturing Journal](https://scholar4ai.com/journals/flexible-services-and-manufacturing-journal.md) | Woo-Jin Shin, Seungkyu Yoon, Hyun-Jung Kim | Gyeongsang National University; Korea Advanced Institute of Science and Technology |
| 2026-10-12 | [Disruption management for large-scale railway networks: A progressive approach with time-phased architecture](https://doi.org/10.1016/j.trc.2026.106059) | [Transportation Research Part C Emerging Technologies](https://scholar4ai.com/journals/transportation-research-part-c-emerging-technologies.md) | Yuehao Zhu, Lingyun Meng, Xiaojie Luan et al. | Beijing Jiaotong University; Roma Tre University |
| 2026-10-12 | [Infrastructure-enabled centralized trajectory planning for lane sorting in mixed-autonomy urban traffic bottlenecks](https://doi.org/10.1016/j.trc.2026.106064) | [Transportation Research Part C Emerging Technologies](https://scholar4ai.com/journals/transportation-research-part-c-emerging-technologies.md) | Qingquan Liu, Kaixuan Tian, Xiangdong Chen et al. | Chongqing University; Tsinghua University; National University of Singapore |
| 2026-10-10 | [A fair profit distribution as a resilient strategy in supply chains under ripple effect](https://doi.org/10.1007/s10696-026-09689-y) | [Flexible Services and Manufacturing Journal](https://scholar4ai.com/journals/flexible-services-and-manufacturing-journal.md) | Tadeusz J. Sawik | Indian Institute of Technology Bombay |
| 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 |  |
| 2026-10-09 | [A Q-Learning-Based hybrid optimization algorithm for storage space allocation and yard Crane cooperative scheduling in double U-shaped Automated container terminals](https://doi.org/10.1016/j.eswa.2026.134517) | [Expert Systems with Applications](https://scholar4ai.com/journals/expert-systems-with-applications.md) | Houming Fan, Wenxin Liu, Hao Fan et al. | Dalian University of Technology; Dalian University; Dalian Maritime University; … |
| 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 | [Resilient agricultural supply chain network design under disruptions with quality deterioration and cold chain integration](https://doi.org/10.1016/j.cie.2026.112444) | [Computers & Industrial Engineering](https://scholar4ai.com/journals/computers-industrial-engineering.md) | Yilan Xu, YANG Yuxiang | China Jiliang University |
| 2026-10-08 | [Decarbonizing oxy-fuel glass furnaces through multi-objective batch and energy planning](https://doi.org/10.1016/j.ijpe.2026.110248) | [International Journal of Production Economics](https://scholar4ai.com/journals/international-journal-of-production-economics.md) | Hossein Arshad, Chiara Caccamo, Thiago Lima Silva et al. | Norwegian University of Science and Technology; SINTEF; SINTEF Energy Research |
| 2026-10-08 | [Virtual formation train timetabling optimization of urban railway networks with rolling stock circulation plan: A coordinate descent-based decomposition method](https://doi.org/10.1016/j.trc.2026.106058) | [Transportation Research Part C Emerging Technologies](https://scholar4ai.com/journals/transportation-research-part-c-emerging-technologies.md) | Nan Zheng, Yin Yuan, Junlin Song et al. | Beijing Jiaotong University; Hong Kong Polytechnic University |
| 2026-10-08 | [Data-driven optimization for drone-truck delivery network design under stochastic demand and semi-open queuing network](https://doi.org/10.1016/j.eswa.2026.134577) | [Expert Systems with Applications](https://scholar4ai.com/journals/expert-systems-with-applications.md) | Sayed Hamid Hosseini Dolatabadi, Rakesh Chowdhury, Tanveer Hossain Bhuiyan et al. | Texas State University; The University of Texas at San Antonio |
| 2026-10-07 | [Human-centric multi-objective optimization of skill-based multi-manned assembly lines using machine learning–guided reinforcement learning](https://doi.org/10.1016/j.cie.2026.112442) | [Computers & Industrial Engineering](https://scholar4ai.com/journals/computers-industrial-engineering.md) | Mansoureh Naderipour, Fahimeh Tanhaie | Shahid Bahonar University of Kerman; Kosar University of Bojnord |
| 2026-10-07 | [Integrated optimization of collection point selection, UAV routing, and upload scheduling for UAV-aided data collection](https://doi.org/10.1016/j.trc.2026.106061) | [Transportation Research Part C Emerging Technologies](https://scholar4ai.com/journals/transportation-research-part-c-emerging-technologies.md) | Bingjie Liang, Gang Zhong, Yuanzhang Zhao et al. | Nanjing University of Aeronautics and Astronautics; Southeast University; University of Wisconsin–Madison |
| 2026-10-07 | [Extended triangle inequalities for nonconvex box-constrained quadratic programming](https://doi.org/10.1007/s10898-026-01644-3) | [Journal of Global Optimization](https://scholar4ai.com/journals/journal-of-global-optimization.md) | Kurt M. Anstreicher, Diane Puges | University of Iowa; University of Klagenfurt |
| 2026-10-06 | [Dynamic last-mile delivery with fatigue under travel time uncertainty](https://doi.org/10.1016/j.tre.2026.105282) | [Transportation Research Part E Logistics and Transportation Review](https://scholar4ai.com/journals/transportation-research-part-e-logistics-and-transportation-review.md) | 楊立勤, Yu Zhang, Roberto Baldacci et al. | Southwestern University of Finance and Economics; Hamad bin Khalifa University; Southwest Jiaotong University |
| 2026-10-06 | [Optimization modeling in business and government: in honor of Professor John M. Mulvey on his 80th birthday](https://doi.org/10.1007/s10479-026-07445-x) | [Annals of Operations Research](https://scholar4ai.com/journals/annals-of-operations-research.md) | David A. Saunders, Stavros A. Zenios | University of Waterloo; Durham University; University of Cyprus |
| 2026-10-05 | [Time–dependent manned–unmanned collaborative delivery routing with partial charging and locker configuration of unmanned ground vehicles](https://doi.org/10.1016/j.cor.2026.107701) | [Computers & Operations Research](https://scholar4ai.com/journals/computers-operations-research.md) | Wenheng Liu, Ge Feng, Weicun Zhang et al. | Hebei University of Technology |
| 2026-10-05 | [Robust vehicle routing problem with flexible docking drones in humanitarian logistics](https://doi.org/10.1016/j.trc.2026.106048) | [Transportation Research Part C Emerging Technologies](https://scholar4ai.com/journals/transportation-research-part-c-emerging-technologies.md) | Mingze Wu, Xinpeng Geng, Chun Cheng et al. | Dalian Maritime University; Dalian University of Technology; University of Wisconsin–Madison |
| 2026-10-05 | [Spatio-temporal graph reinforcement learning for multi-period supply chain synchronization: Joint procurement, warehousing, and multimodal routing with multiple 3PL providers](https://doi.org/10.1016/j.cor.2026.107697) | [Computers & Operations Research](https://scholar4ai.com/journals/computers-operations-research.md) | Jinjin Cai, Rui Song, 何世伟 et al. | Beijing Jiaotong University |
| 2026-10-05 | [Beyond productivity: Does ICT agglomeration drive regional eco-efficiency?](https://doi.org/10.1016/j.strueco.2026.09.009) | [Structural Change and Economic Dynamics](https://scholar4ai.com/journals/structural-change-and-economic-dynamics.md) | Maria Chiara D’Errico, Anna Maria Ferragina, Stefano Iandolo et al. | University of Perugia; University of Salerno; École Supérieure du Commerce Extérieur; … |

## Cite this page

Scholar4AI. (2026). Linear and integer programming. Journal Research Rankings. Retrieved October 26, 2026, from https://scholar4ai.com/equations/linear-and-integer-programming

```bibtex
@misc{scholar4ai-equations-linear-and-integer-programming,
  author = {{Scholar4AI}},
  title = {Linear and integer programming},
  year = {2026},
  howpublished = {\url{https://scholar4ai.com/equations/linear-and-integer-programming}},
  urldate = {2026-10-26},
  note = {Journal 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/).