Consider an arc that carries
flow between two nodes. We learn that the first 10 units
of flow have a unit cost of $5, the next 5 units of
flow have a cost of $8, and any additional amount has
a cost of $10. |

With unit cost is increasing with flow, the arc cost
is a convex function of flow. Fig. 25 shows a linear model
that has an arc for each level of unit cost. In cases
where the cost function is continuous, the model uses
a piecewise linear approximation with the number of arcs
determining the accuracy of the approximation. Concave
cost functions cannot be addressed with linear models.

Nonlinear concave revenue functions can be handled in
a similar way. The revenues are represented with negative
arc costs.

Figure 25. Representation of nonlinear costs