I want to write constraints for finding a path for some rider, driver on a directed network problem.
Let $x_{i,j}^d$ indicate whether driver travels from $i$ to $j$ and $z_{i,j}^{r,d}$ indicates whether riders travel from $i$ to $j$ with driver, and finally, let $y_{i}^{r,d}$ indicate whether driver picks up at $i$ the rider.
I want to ensure that if a driver wants to pick up someone at $i$, then they should travel on an edge connected to $i$. Is this way of writing correct?
$$ y_{i}^{r,d} = 1 \implies \sum_{j: (i,j) \in links} x_{i,j}^d =1$$
Then how to linearize this? Is this even correct?
$$ y_{i}^{r,d} \le \sum_{j: (i,j) \in links} x_{i,j}^d $$
And, more generally, is there any good resource that explains these linearization techniques very easily and comprehensively? I've searched and everywhere is not complete and easy to understand.
Your linear constraint enforces $$y_{i}^{r,d} = 1 \implies \sum_{j: (i,j) \in links} x_{i,j}^d \ge 1$$ Do you already have other constraints $$\sum_{j: (i,j) \in links} x_{i,j}^d \le 1?$$ If so, then your proposed linearization is sufficient.
For many linearization examples and links to references, see the [linearization] tag on the Operations Research StackExchange.