Timed Weighted Event Graphs (in short TWEG) are widely used for modeling industrial problems or embedded systems. The aim of this paper is to develop polynomial algorithms to check the existence of periodic schedules and to compute their optimal throughput. A necessary and sufficient condition of existence of periodic schedules is first expressed. Then, we develop an algorithm to compute the optimal throughput of a periodic schedule. This theoretical work can be considered as a generalisation of Reiter's result ("Scheduling Parallel Computations", R. Reiter, JACM, 1968). The gap between the optimal throughput of a TWEG and the throughput of an optimal periodic schedule is also experimentally investigated for a circuit.