I am relatively new to the topic of optimization. I am currently trying to address the following problem:
We are given a set of jobs, say $J$ with release times, deadlines and duration. Jobs can be pre-empted and also can be scheduled to run in parallel on different machines with the only constraint that a unit of a given job (from its duration) cannot be proccessed at the same time on 2 different machines. Objective is to find the minimum amount of machines required for a feasible schedule to be possible (not the schedule itself).
I am seeking a polynomial time solution. Is someone aware of such problem in the literature?