Going from Gross Cash Flow to Net Cash Flow without introducing Non-Linearity?

Hi @Baste. I assume that P_TaxationRate is a number between 0 and 1. If the model (indirectly) maximizes V_NetCashFlow then you can use the following. Introduce two nonnegative variables V_GrossCashFlowPos and V_GrossCashFlowNeg, and define V_GrossCashFlow as:

Variable V_GrossCashFlow {
    Range: free;
    Definition: V_GrossCashFlowPos - V_GrossCashFlowNeg;
}

Then V_NetCashFlow can be defined as:

Variable V_NetCashFlow {
    Range: free;
    Definition: V_GrossCashFlowPos *  (1 - P_TaxationRate) - V_GrossCashFlowNeg;
}

If the model (indirectly) maximizes V_NetCashFlow then either V_GrossCashFlowPos or V_GrossCashFlowNeg will be 0.

This is not sufficient if the model (indirectly) minimizes V_NetCashFlow because then V_GrossCashFlowPos and V_GrossCashFlowNeg both will be non-zero, resulting in an incorrect value for V_NetCashFlow. In that case a new binary variable V_Bin is needed to enforce that V_GrossCashFlowPos and V_GrossCashFlowNeg cannot both be non-zero. This binary variable is then used in two new constraints:

Constraint c1 {
    Definition: V_GrossCashFlowPos <= M * V_Bin;
}
Constraint c2 {
    Definition: V_GrossCashFlowNeg <= M * (1 - V_Bin);
}

Here ‘M’ is some big number.