This paper considers the problem of deriving an optimal periodic schedule for general multipurpose plants comprising batch, semi-batch and continuous operations. This involves the determination both of the optimal duration of the operating cycle, and of the precise nature and timing of operations taking place within it. The basis of our formulation is the general resource-task network (RTN) process representation coupled with a continuous representation of time; The presented mathematical formulation results in a mixed integer non-linear programming (MINLP) problem which cannot be linearized exactly. We describe a special branch-and-bound algorithm for solving this problem by branching on both discrete and continuous variables. The overall approach can be parallelized in an effective manner as demonstrated by the examples presented.