Timed event graphs (TEGs) and timed weighted event graphs (TWEGs), which have multiple arc cardinalities, have been widely used for automated production systems such as robotic work cells or embedded systems. TWEGs are useful for modeling batch flows of entities such as batch arrivals or processing of jobs. Periodic schedules, that combine an explicit description of starting times and an easy implementation, are particularly interesting, and have been proved to be optimal for ordinary timed event graphs (TEGs). In this paper, we present polynomial algorithms to check the existence of periodic schedules of bounded TWEGs and to compute their optimal throughput. These results can be considered as generalizations of those for ordinary timed event graphs. We then establish that periodic schedules are suboptimal for TWEGs and may not exist even for a live TWEG. The gap between optimal throughput and throughput of an optimal periodic schedule is experimentally investigated for a subclass of TWEGs, namely timed weighted circuits.