How can I express the process of converting a series of if-then constraints into a linear form?
Let's assume that we have integer variable $x_i$, non-negative variables $y_i^d$, and binary variables $\delta_{i,j}^d$. Additionally, we assume that N and S are natural numbers, and A and B are subsets of all links $(i,j) \in E$, where A and B represent links that do not intersect.
The conditional statements:
If $x_i \geq N $ then The $\delta_{i,j}^d = 1 $ or $ \delta_{i,j}^d = 0$. but if $\delta_{i,j}^d = 1$ I want to ensure that $ y_i^d \leq y_j^d - S \quad \forall (i,j) \in A$
But If $x_i < N $ I want to ensure that $\delta_{i,j}^d=0 \quad \forall (i,j) \in A$ but they could take value fron set$B$. in other words, $\delta_{i,j}^d =0 $ or $ \delta_{i,j}^d =1 \quad \forall (i,j)\in B $ And if this latter happen $ y_i^d \leq y_j^d - N \cdot S \quad \forall (i,j)\in B $