{"id":20556532,"url":"https://github.com/somjit101/min-cost-network-flow-lemon","last_synced_at":"2025-07-06T15:04:44.907Z","repository":{"id":179925219,"uuid":"375562804","full_name":"somjit101/Min-Cost-Network-Flow-Lemon","owner":"somjit101","description":"A Simple C++ Implementation of the Lemon Optimization Library to Solve a Minimum Cost Flow problem in a given Graph Network with Supply/Demand Values of Nodes and Capacity, Unit Cost of Flow for each Edge.  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Follow the [instructions](https://lemon.cs.elte.hu/trac/lemon/wiki/InstallGuide) to build and install the library on your programming environment.\n\n## Problem Definition\nA minimum cost flow problem is where a real-world network of physical locations is represented by a Graph in the following manner : \n* **Nodes** - represent each physical location associated with a certain amount of Supply (+ve value) or Demand (-ve value)\n* **Edges** -  Connects nodes as per per available routes for real-world resource transfer. Each edge is associated with a certain max capacity of transfer and a cost of transfer per unit of resource\n\n**For the purpose of demonstration we have used a simple problem illustrated on the Google OR Tools webpage found [here](https://developers.google.com/optimization/flow/mincostflow) :**\n\n![Probelm Figure](Problem_Figure.jpg)\n\nIn the above figure :\n* The no. on each Node represents the Supply/Demand value at each location.\n* The black no. on each Edge represents the cost of transfer of resources per unit.\n* The red no. underneath each Edge represents the maximum flow capacity.\n\n**The problem data has been recorded as per requirement in .csv format to be read by the program.** \n\n\n## Objective\nReturn a list of optimal flows for each edge in the directed graph to minimize the gap between the supply and demand at the minimum attainable transfer cost. \n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fsomjit101%2Fmin-cost-network-flow-lemon","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fsomjit101%2Fmin-cost-network-flow-lemon","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fsomjit101%2Fmin-cost-network-flow-lemon/lists"}