Theoretical BackgroundΒΆ

Minimum Cost Flows

\[\begin{split}\begin{align*} \min \text { } & C(\mathbf{x}) \\ \text {s.t.} \quad \mathbf{\Gamma} \mathbf{x} &= \mathbf{b}, \\ \mathbf{x} &\geq \mathbf{0} \end{align*}\end{split}\]

Parametric Minimum Cost Flows

Find minimum cost flows for parametric demands \(\mathbf{h}(\lambda)\) with \(\lambda \in \left[0, \lambda^{\max }\right]\)