Electric arc furnaces (EAFs) are widely applied in the steel industry for producing steel by melting scrap metal. This highly energy-intensive steelmaking process is subject to limited automation, with decisions related to input amounts and timings typically made by operators. This leads to suboptimal EAF batch operation due to complex behavior and relationships between variables that are inevitably overlooked in the decision making. In this work, we introduce an advisory system that employs a first-principles EAF model to support the operator decision making in real-time for economically optimal process operation. A dynamic optimization calculation can be triggered by the operator at any point in the batch, an action that can be repeated multiple times during the batch. The advisory system incorporates a multirate moving horizon estimator (MHE) that continually computes estimates of the process states utilizing current and past inputs and measurements. End-point constraints and potential extension of the batch duration are handled through a multitiered optimization algorithm. Case studies demonstrate a major economic improvement when the dynamic optimization-based advisory system is used. We show that the online computational load is under 5 s on average when a proposed multitiered initialization scheme is used for solving the large-scale optimal control problems.