# Network Flow Pt.2

In the previous network flow model, the cost of an edge is linear:

\text{Cost of arc }i\to j = c_{ij}x_{ij}

Suppose now there’s a starting price d_{ij} to send any amount of flow on arc i\to j.

Let non-negative x_{ij} be the flow of i\to j.

We can model the initial cost with an indicator variable y_{ij}.

y_{ij} = \begin{cases}
1 & \text{if need to pay to send flow on }i\to j\\
0 & \text{otherwise}

\end{cases}

The total cost/objective function becomes:

\min\sum_{(i\to j)\in A}c_{ij}x_{ij} + \sum_{(i\to j)\in A}d_{ij}y_{ij}