We study here the problem of scheduling unit-time jobs with release and due dates on identical machines while meeting a non-idling constraint and minimizing the number of active machines. Though this problem is theoretically solvable in polynomial time, designing an efficient algorithm remains an issue. We establish here several theoretical results that allow us to break symmetries and significantly reduce the search space, before designing and testing a very efficient A∗ like algorithm involving constraint propagation, which outperforms standard approaches based upon ILP formulations.