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I was hoping to get some help in modelling the following logic as an MIP Constraint
If $X_{ij}=1$ and $\text{SDV}_{ikj}=1$ for a particular index $i$, then $\text{SOC}^L_i=100$, else $\text{SOC}^L_i$ can take any value.
$X_{ij}$ and $\text{SDV}_{ikj}$ are binary decision variables, while $\text{SOC}^L_i$ is a system variable.
I figured it would use some kind of Big M formulation but I am not sure how. Thank you in advance!
$$\text{SOC}_i^L \ge 100 - M \times (1- X_{i,j}) - M \times (1- \text{SDV}_{i,k,j})$$ $$\text{SOC}_i^L \le 100 + M \times (1- X_{i,j}) + M \times (1- \text{SDV}_{i,k,j})$$
When $X_{i,j} = 1$ and $SDV_{i,k,j} = 1$ the two equations above will end up becoming:
$$\text{SOC}_i^L \ge 100 $$ $$\text{SOC}_i^L \le 100 $$
Otherwise, the range of $\text{SOC}_i^L$ will be $[-M, +M]$.
More generally, if $s\in[L,U]$, you can model $(x=1 \land y=1) \implies s=C$ (constant $C$) as follows: $$ x + y - 1 \le z\\ (L-C)(1-z) \le s - C \le (U-C)(1-z)\\ z\in\{0,1\} $$ This approach introduces an additional binary variable and constraint beyond @anoopyadav's model but avoids $2M$.
