Min-cost flow network model
A standard min-cost flow network model, formulated as a linear programming model, can look like:
| Model 1: standard min-cost flow network model |
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| \[\begin{align}\min& \sum_{(i,j)\in A}\color{darkblue}c_{i,j}\cdot\color{darkred}f_{i,j}\\ & \sum_{j|(j,i)\in A}\color{darkred}f_{j,i} + \color{darkblue}{\mathit{supply}}_i = \sum_{j|(i,j)\in A}\color{darkred}f_{i,j} + \color{darkblue}{\mathit{demand}}_i && \forall i \\ & \color{darkred}f_{i,j} \in [0,\color{darkblue}{\mathit{capacity}}_{i,j}] \end{align}\]
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