Solve statement workflow

This part of the code includes the perfect-foresight, myopic and rolling-horizon model solve statements including the required accounting of investment costs beyond the model horizon.

Perfect-foresight model

For the perfect foresight version of MESSAGEix, include all years in the model horizon and solve the entire model. This is the standard option; the GAMS global variable %foresight%=0 by default.

\[\min_x \text{OBJ} = \sum_{y \in Y} \text{OBJ}_y(x_y)\]

Recursive-dynamic and myopic model

For the myopic and rolling-horizon models, loop over horizons and iteratively solve the model, keeping the decision variables from prior periods fixed. This option is selected by setting the GAMS global variable %foresight% to a value greater than 0, where the value represents the number of years that the model instance is considering when iterating over the periods of the optimization horizon.

Loop over \(\hat{y} \in Y\), solving

\[\begin{split}\min_x \ \text{OBJ} = \sum_{y \in \hat{Y}(\hat{y})} \text{OBJ}_y(x_y) \\ \text{s.t. } x_{y'} = x_{y'}^* \quad \forall \ y' < y\end{split}\]

where \(\hat{Y}(\hat{y}) = \{y \in Y | \ |\hat{y}| - |y| < \text{optimization_horizon} \}\) and \(x_{y'}^*\) is the optimal value of \(x_{y'}\) in iteration \(|y'|\) of the iterative loop.

The advantage of this implementation is that there is no need to ‘store’ the optimal values of all decision variables in additional reporting parameters - the last model solve automatically includes the results over the entire model horizon and can be imported via the ixmp interface.