Efficient frameworks for scheduling of energy-intensive industries are important enablers for the industrial implementation of the demand-side management concept (DSM). DSM enables enterprises to cut their energy cost as well as to support the grid in dealing with fluctuating availability of energy. In this work, we present an improvement of the energy-aware production scheduling strategy reported in Hadera et al.,(1) which is based upon a continuous-time scheduling formulation. The improvement concerns the modeling of the coupling between the scheduling problem and the computation of the energy bill. The resulting optimization problem is solved by the heuristic bilevel decomposition from Hadera et al.(2) Numerical studies showed that although the proposed formulation and heuristic decomposition does not guarantee to obtain the global minimum it does provide good quality solutions within reasonable solution times. The new energy-awareness formulation reduces the number of binary variables and constraints and results in shorter solution times.