The main objective of this work is the development of a computational procedure for determining optimal operating strategies for an industrial electric arc furnace (EAF). These goals are achieved by incorporating a detailed mechanistic model into a mathematical optimization framework. The model used in this work includes mass and energy balances, and contains sufficient detail to describe the melting process, chemical changes, and material and energy flows. Mathematical optimization is used to determine the optimal input trajectories based on an economic criterion; process limitations are accounted for by including them within the optimization problem as constraints. This optimization procedure considers trade-offs between all the process inputs and processing time, so as to maximize the profit. Several case studies illustrating the use of mathematical optimization in the enhancement of process performance are given.