As a major energy consumer, steel plants can help stabilize the
power grid by shifting production from periods with high demand. Electric
arc furnaces can be operated at different power levels, affecting
the energy efficiency, the duration of melting tasks, and the rate
of electrode degradation, which has previously been neglected. We
thus propose a new mixed-integer linear programming (MILP) formulation
for optimal scheduling under time-of-use electricity pricing that
captures the tradeoffs involved. It relies on the resource-task network
(RTN) for modeling processing tasks with variable electrode mass depletion
and replacement tasks that regenerate the mass. Results for an industrial
case study show that the high-power mode, which allows for faster
execution and to fit more tasks in low-price periods but is the least
energy-efficient and consumes the largest mass of electrode, is mostly
avoided. It indicates that electrode replacement plays an important
role in total cost minimization.