--- title: Min-Cost Flow | SpinForge url: https://spin-forge.com/solvers/min-cost-flow description: Solve minimum-cost network flow exactly, with every optimum independently verified. --- Garmo Solvers SPINFORGE / A GARMO LABS COMPANY # Min-Cost Flow Solve minimum-cost network flow exactly, with every optimum independently verified. [Explore the family](https://spin-forge.com/solvers) [Talk about your workload](https://spin-forge.com/contact) Customer outcome [Build better plans and decisions](https://spin-forge.com/platform/checked-decisions) GARMO SOLVERS · S17 ## [Exact Min-Cost Flow Against OR-Tools](https://spin-forge.com/proof/s17) 1.2-2.5x faster on medium instances 100% optima verified behind on large NETGEN exact integer arithmetic [Full result, charts and conditions](https://spin-forge.com/proof/s17) THE PRODUCT, IN PRACTICE ## Solve min-cost flow exactly and verify the optimum Solve minimum-cost network flow exactly, with every optimum independently verified. It is a newer Garmo Solvers module from the October 2026 benchmark campaign, outside the 1.0.2 release. Results are checked against the original input; the measured result below states where it is ahead and where it is not. BUILT FOR Logistics, supply-chain, telecom and planning teams with network-flow workloads. CHALLENGES PRODUCT RESPONSE ## The problem you face. What the product changes. YOUR CHALLENGE WITH MIN-COST FLOW 01 ### The problem needs the right operation A min-cost flow network in DIMACS format. Solve minimum-cost network flow exactly, with every optimum independently verified. 02 ### A result must answer the original question An answer detached from its original constraints or input is difficult to rely on. The suite rechecks the answer against the original input and identifies the applicable result state. 03 ### The comparison needs a defined scope A capability or benchmark result is not a universal promise for a different workload. Evaluate the selected input, resource budget, complete cost and required certificate against your baseline. WHAT YOU GET ## A defined capability. A useful result. 01 ### Selected solving capability Solve minimum-cost network flow exactly, with every optimum independently verified. 02 ### Original-input result An integer optimal flow in exact integer arithmetic, with an independent optimality check. 03 ### Common access Run it as garmo netflow or through the garmo-mcp server; headless execution fits scripts and automated workflows. 04 ### Checked result Every optimum is verified independently of the network simplex that produced it. GARMO SOLVERS / MEASURED RESULT ## Measured: 1.2-2.5x faster on medium Exact integer network simplex. On medium SR instances (2^13 to 2^15 nodes) it is 1.2-2.5x faster than OR-Tools, with every optimum verified; on large NETGEN-8 (2^17) it takes 9-12 s against 4.4 s for OR-Tools. Source: Garmo Labs benchmark campaign, October 2026. Results apply to the stated inputs, hardware and conditions; they are not universal competitor rankings. [See the measured result and charts](https://spin-forge.com/proof/s17) EXAMPLE CUSTOMER WORKFLOW ## Use Min-Cost Flow in a defined workflow A customer has a supported model and wants an accepted result without adopting every other module. Illustrative customer use—not a new benchmark or completed customer deployment. 1. 01 Provide the original input and define the useful outcome. 2. 02 Run the selected module under its supported resource and interface scope. 3. 03 Review the returned answer, original-input checks and completion state. FIT & ACCEPTANCE ## Start with the task. Agree the useful outcome. What you bring A min-cost flow network in DIMACS format. What a useful evaluation measures - + Accepted original-model result - + Appropriate certificate or disclosed uncertified state - + Total time, memory and operating cost Delivery License the selected capability, commission an implementation, or agree an operated service. Infrastructure and additional engineering are specified separately. QUESTIONS BEFORE BUYING ## A clear scope. A clear relationship. **What is the important boundary? − **OR-Tools is faster on the large NETGEN instances reported. **How is it priced? + **No new standalone price is supplied for this product; request a scoped proposal. The platform plans buy qualified workflows and capacity, not a second charge every time a compatible method is selected. Existing bundle inclusions do not expand automatically. **How do we get access? + **Available through garmo CLI and garmo-mcp, including headless execution. Product-specific inputs, runtime dependencies, budgets and result checks remain explicit. PUT THE PRODUCT TO WORK ## Tell us what needs to improve. Bring a task, an accepted outcome and the environment in which the product needs to work. [Discuss this workflow ](https://spin-forge.com/contact?product=solvers%2Fmin-cost-flow&brief=Product%3A+Min-Cost+Flow%0AOur+challenge%3A%0AOur+workload%2Finput%3A%0AExpected+result%3A%0AAcceptance%3A+Accepted+original-model+result%3B+Appropriate+certificate+or+disclosed+uncertified+state%3B+Total+time%2C+memory+and+operating+cost%0AEnvironment+and+delivery+preference%3A%0A) PRODUCT RELATIONSHIPS ## Related, not interchangeable. [RELATED PRODUCT ### UNISOLVE One headless solver platform for compatible method selection, mixed-capability solving and source-bound result checks.](https://spin-forge.com/unisolve) ONE PLATFORM ## Choose a qualified workflow. Select the capability you need directly or include its compatible role in a qualified platform workflow. Production scope identifies release, environment, capacity and support; a product count is not an entitlement. [Explore monthly plans](https://spin-forge.com/plans) [See the system connections](https://spin-forge.com/system-synergies/product-map) START WITH THIS PRODUCT Use the software directly or ask us to scope the implementation. [Software access](https://spin-forge.com/plans?product=solvers/min-cost-flow) [Have us do the work](https://spin-forge.com/contact?product=solvers/min-cost-flow&delivery=engineering)