In this paper we study a problem with periodic time slots in which a processing time and periodically repeating due dates are given for each job, where the period is the same for all jobs. The objective is to minimize the number of periodic time slots in which all jobs can be scheduled just-in-time. We show that when set-up times between jobs are considered, the problem becomes unary NP-hard even in the single machine case. When set-up times are not considered, we study several subproblems which arise by putting additional restriction on processing times. We show that under a rather strict (although natural) restriction the problem is solvable in polynomial time for an arbitrary number of identical parallel machines, and we present a simple polynomial time algorithm solving the problem. We also show, that when the restriction on processing times is lifted, the problem without set-up times becomes binary NP-hard already for two machines and unary NP-hard when the number of machines is a part of the input.