Spillage

Spillage paths go from a hydraulic node (Reservoir, Junction) to another (including the sea). The spillage pathway is used when no other alternative is available. Use of the spillage path represents water overflowing the reservoir. The spillage variable is essentially a slack variable for the reservoir balance, given overflow.

\[\begin{split} \\{i \in reservoirs,\ k \in \\{0, 1, ..., timesteps - 1\\}\\}\end{split}\]

\[ 0 \leq spi(i,k) \]

Spillage incurs a cost that should be higher than the use of any other paths.

\[ Obj^{min}: C^Tx + \sum{{C^T}_{spi}(i,k)*spi(i,k)} \]