There are $N$ types of jobs. For each $i$, we have to schedule $T/D_i$ jobs of type $i$ in $T$ timeslots. We know that $\sum_{i=1}^N 1/(D_i+1) = 1$. For each type $i$, the distance between two consecutive jobs of type $i$ should be greater than $D_i$. This is the separation constraint.
Is there any related literature for this scheduling problem? Specifically, what is the hardness of the above scheduling problem?
EDIT: I found that the pinwheel scheduling is similar to this problem where the constraint is type $i$ job appears at least once in every $(D_i+1)$ timeslots with $\sum_{i=1}^N 1/(D_i+1) < 1$. However, a pinwheel schedule does not necessarily satisfy the Separation constraint in this case.