# End valuation with Benders cuts (Benders module)

Values are supplied through Benders cuts from a process such as Fansi or Scenario Fan. At the moment these values are supplied from Fansi. Cuts are created in the form of a number of constraints added to the LP-model:

$$ \\{i \in reservoirs,\ k = timesteps-1,\ n \in \\{0, 1, ..., num\\_cuts - 1\\}\\}$$

$$ \textrm{ALPHASUM}(n):\alpha - \sum_{i}^{reservoirs} \textrm{WaterValue}(i)*res(i,k) \geq \textrm{CutRhs}(n)  $$

$$ -\infty \leq \alpha \leq \infty $$

The total value of the water is added to the objective function, where alpha will be negative:

$$ Obj^{min}: C^Tx + \alpha $$

**Note: Target reservoirs do not get an end valuation.**