# Is there a better way to formulate this constraint?

Let $$x_{r}^{j}=1\iff$$ the machine schedules job $$j$$ using resource $$r$$. My constraint says that: a resource cannot be used twice, i.e., if $$x_{r}^{j}=1$$, then $$x_{r}^{j'}=0$$ for $$j'\neq j$$. I write this as: $$x_{r}^{j}+x_{r}^{j'}\leq1,\forall j\neq j', \forall r.$$

Is there a better way to formulate this?

You can strengthen your "conflict" constraint to a "clique" constraint: $$\sum_j x_r^j \le 1$$ for all $$r$$. There are fewer of these, and they dominate the conflict constraints.
Same idea, but typically formulated as $$\sum_j x_r^j \leq 1, \: \forall r$$ For binary $$x$$