How do I implement a non-balanced MCF problem in MATLAB?

Dipak Narayan

2017 10 23

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I have to implement minimum cost flow on MATLAB. When my problem is balanced, I'm able to solve the problem using intlinprog of Optimization Toolbox. However when the problem is unbalanced the code throws an error which is understandable.

"Solver stopped prematurely. No integer feasible point found.

Intlinprog stopped because it exceeded the iteration limit while solving the root LP problem, options.RootLPMaxIterations = 30000 (the default value)."

I've read that adding ground nodes to the graph solves the problem (with the excess/deficit of the node set accordingly) However, how do I code the ground node given that I do not have apriori knowledge about the graph?