This work proposes a general discrete-time simultaneous scheduling and dynamic optimization (SSDO) formulation based on the state-task network (STN) representation. This formulation explicitly considers variable processing times, which is a key aspect in the integration of scheduling and control decisions. The resulting Mixed-Integer Nonlinear Programming (MINLP) problem is solved using a custom Discrete-Steepest Descent Algorithm (D-SDA), which is designed to efficiently explore the ordered discrete decisions in the formulation, i.e., processing times and batching variables. The performance of the proposed solution framework is illustrated using two case studies adapted from the literature. The results show that the D-SDA explores the feasible region of ordered discrete decisions more efficiently than a general-purpose MINLP solver, leading to more profitable solutions in shorter computational times.