Build on research,
proven in practice
The research behind Flowty’s path-based multi-commodity flow solver
The Flowty multi-commodity flow (MCF) solver is grounded in deep academic insight into the structure and complexity of MCF problems. Our team's foundational research has tackled some of the most difficult variants of MCF—problems so complex they are typically out of reach for general-purpose solvers.
In particular, our co-founders have authored research papers advancing algorithmic techniques for multi-commodity flow problems, including Dantzig–Wolfe decomposition, column generation and branch-and-price algorithms tailored to the unique structure of MCF models.
One study by Brouer, Pisinger and Spoorendonk [1] tackled real-world liner shipping networks with over 25,000 demands and hundreds of ports, solving relaxed MCF instances to near-integer optimality in under an hour, remarkably fast for problems of this scale. This was achieved using path-flow models and efficient column generation techniques that now underpin key components of Flowty's solver architecture.
Another by Gamst and Petersen [2] demonstrated how custom decompositions and tailored branching strategies could solve challenging k-splittable MCF problems more efficiently and reliably than any off-the-shelf solver, even when the solution space was vast and highly constrained. This research foundation gives Flowty a unique advantage: We understand the theoretical limits of flow optimisation and repeatedly show we can push beyond them.
The result is a solver that doesn't just run; it scales and outperforms on real-world networks. And because we deeply understand these problems, we can adapt them to handle the complexities that arise in practice.
References
[1] Brouer, B. D., Pisinger, D., & Spoorendonk, S. (2011). Liner Shipping Cargo Allocation with Repositioning of Empty Containers. INFOR: Information Systems and Operational Research, 49(2), 109–124. https://doi.org/10.3138/infor.49.2.109
[2] Gamst, M., & Petersen, B. (2012). Comparing Branch-and-Price Algorithms for the Multi-Commodity k-splittable Maximum Flow Problem. European Journal of Operational Research, 217(2), 278-286. https://doi.org/10.1016/j.ejor.2011.10.001
The research behind Flowty’s path-based multi-commodity flow solver
The Flowty multi-commodity flow (MCF) solver is grounded in deep academic insight into the structure and complexity of MCF problems. Our team's foundational research has tackled some of the most difficult variants of MCF—problems so complex they are typically out of reach for general-purpose solvers.
In particular, our co-founders have authored research papers advancing algorithmic techniques for multi-commodity flow problems, including Dantzig–Wolfe decomposition, column generation and branch-and-price algorithms tailored to the unique structure of MCF models.
One study by Brouer, Pisinger and Spoorendonk [1] tackled real-world liner shipping networks with over 25,000 demands and hundreds of ports, solving relaxed MCF instances to near-integer optimality in under an hour, remarkably fast for problems of this scale. This was achieved using path-flow models and efficient column generation techniques that now underpin key components of Flowty's solver architecture.
Another by Gamst and Petersen [2] demonstrated how custom decompositions and tailored branching strategies could solve challenging k-splittable MCF problems more efficiently and reliably than any off-the-shelf solver, even when the solution space was vast and highly constrained. This research foundation gives Flowty a unique advantage: We understand the theoretical limits of flow optimisation and repeatedly show we can push beyond them.
The result is a solver that doesn't just run; it scales and outperforms on real-world networks. And because we deeply understand these problems, we can adapt them to handle the complexities that arise in practice.
References
[1] Brouer, B. D., Pisinger, D., & Spoorendonk, S. (2011). Liner Shipping Cargo Allocation with Repositioning of Empty Containers. INFOR: Information Systems and Operational Research, 49(2), 109–124. https://doi.org/10.3138/infor.49.2.109
[2] Gamst, M., & Petersen, B. (2012). Comparing Branch-and-Price Algorithms for the Multi-Commodity k-splittable Maximum Flow Problem. European Journal of Operational Research, 217(2), 278-286. https://doi.org/10.1016/j.ejor.2011.10.001
The research behind Flowty’s path-based multi-commodity flow solver
The Flowty multi-commodity flow (MCF) solver is grounded in deep academic insight into the structure and complexity of MCF problems. Our team's foundational research has tackled some of the most difficult variants of MCF—problems so complex they are typically out of reach for general-purpose solvers.
In particular, our co-founders have authored research papers advancing algorithmic techniques for multi-commodity flow problems, including Dantzig–Wolfe decomposition, column generation and branch-and-price algorithms tailored to the unique structure of MCF models.
One study by Brouer, Pisinger and Spoorendonk [1] tackled real-world liner shipping networks with over 25,000 demands and hundreds of ports, solving relaxed MCF instances to near-integer optimality in under an hour, remarkably fast for problems of this scale. This was achieved using path-flow models and efficient column generation techniques that now underpin key components of Flowty's solver architecture.
Another by Gamst and Petersen [2] demonstrated how custom decompositions and tailored branching strategies could solve challenging k-splittable MCF problems more efficiently and reliably than any off-the-shelf solver, even when the solution space was vast and highly constrained. This research foundation gives Flowty a unique advantage: We understand the theoretical limits of flow optimisation and repeatedly show we can push beyond them.
The result is a solver that doesn't just run; it scales and outperforms on real-world networks. And because we deeply understand these problems, we can adapt them to handle the complexities that arise in practice.
References
[1] Brouer, B. D., Pisinger, D., & Spoorendonk, S. (2011). Liner Shipping Cargo Allocation with Repositioning of Empty Containers. INFOR: Information Systems and Operational Research, 49(2), 109–124. https://doi.org/10.3138/infor.49.2.109
[2] Gamst, M., & Petersen, B. (2012). Comparing Branch-and-Price Algorithms for the Multi-Commodity k-splittable Maximum Flow Problem. European Journal of Operational Research, 217(2), 278-286. https://doi.org/10.1016/j.ejor.2011.10.001