This paper presents a new mixed integer nonlinear program (MINLP) model for the periodic scheduling of multistage, multiproduct continuous plants featuring equipment units in parallel that are subject to sequence dependent changeovers. The formulation is based on the resource task network (RTN) process representation, features combined processing and changeover tasks, and assumes that each order is executed only once on each stage. The new multiple time grid formulation is compared to an also RTN-based, single time grid formulation, through the solution of a few example problems taken from the literature. The results show that the proposed formulation is significantly more efficient computationally, essentially because smaller problems are generated and, because the number of tasks to execute can easily be predicted, no iterative procedure over the total number of event points in the time grid is required to find the optimal solution. On the other hand, the single time grid formulation is able to sometimes find better solutions to the problem because of its ability to consider, for each order, the execution of more than a single instance of the processing task per stage.