This paper considers the problem of determining an optimal periodic schedule for multipurpose plants comprising batch, semi-batch and continuous operations. This aims to determine both the optimal duration of the operating cycle, and the precise nature and timing of operations taking place within it. The basis of our formulation is the general Resource-Task Network process representation coupled with a continuous representation of time. The presented mathematical formulation results in a non-convex mixed integer nonlinear programming (MINLP) problem. The paper describes a special branch-and-bound algorithm for solving this problem by branching oil both discrete and continuous variables. The overall approach is demonstrated with an example.