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Scheduling is a main issue of real-time systems because it involves meeting the deadlines. In this paper, we address the problem of scheduling a set of periodic tasks on m processors under EDF (Earliest Deadline First) using a partitioned scheme. The allocation problem is transformed into a binary integer linear program. Then, it is solved by applying Geoffrion's version of Balas' additive method, optimized for the real-time scheduling problem. In order to assess the feasibility of the approach for a small size practical problem, some experimental results are shown.