Let $x_{j}(t)=1$ iff job $j$ is scheduled at time $t$. I want to say that if the job is scheduled at all, then it is scheduled at $n_j$ slots. I wrote this as:
$$x_{j}(t)\sum_{s=1}^{T}x_{j}(s)=n_jx_{j}(t).$$
Is it possible to write this as linear constraints?
If I am maximizing the number of jobs to be scheduled, can we do any better?