The minimization of the amount of initial tokens in a Weighted Timed Event Graph (in short WTEG) under throughput constraint is a crucial problem in industrial area such as the design of manufacturing systems or embedded systems. In this paper, an efficient polynomial algorithm is developed for the minimization of the overall places capacities with a maximum throughput. It is proved optimal for a particular sub-classes of WTEG and is leading to a 2-approximation solution in the general case.