Energy is becoming a critical resource for process industries as introduction of new policies drive changes in the energy supply systems. Energy availability and pricing is much more volatile. In this study, we propose a Mean Value Cross Decomposition approach to functionally separate production scheduling from energy-cost optimization. Such a decomposition makes it possible to exploit existing optimization solutions avoiding a need to create a new monolithic model. The proposed framework is applied to a continuous process of thermo-mechanical pulping using a discrete-time Resource-Task Network model. Example case study scenarios show that the approach gives optimal system-wide solutions while keeping the models separated.