Production scheduling is the main driver of the production performance. Nowadays, manufacturers should consider not only the economic factors but also the sustainability for the production scheduling. This means that a production schedule should ensure the cost efficiency, more usage of green energy, and less CO2 emission. Designing a scheduling system that considers both sustainability and economic factors requires a smart manufacturing environment that integrates proprietary data sources for data ubiquity. In addition, the scheduling system should be able to derive solutions in a reasonable amount of time. The scheduling system should be modifiable so that it can be applied to different production situations with less effort. To address the above challenges, we present the architecture of a scheduling system for energy-optimized production. Digital twins are adopted to ensure the interoperability of the scheduling system. A Monte Carlo based scheduling method is used to derive near optimal schedules. The Monte Carlo based scheduling method is generic and can be easily configured for a specific application. To accelerate the computation, we plan to deploy the scheduling system on a supercomputer and parallelize the computation as much as possible. Our work will provide a configurable scheduling service for firms to solve small and medium-sized scheduling problems.