A system that generates brewed beverages may receive requests to produce specified brewed beverages. The system may include a scheduler that initiates and controls the performance of one or more chemical or mechanical processes to produce the beverages. While one chemical or mechanical process for producing a beverage is being performed, other processes may be performed for production of the beverage or another beverage. The scheduler may determine the time at which to perform each process, the time at which a beverage should be presented, the resources to be used to perform the processes, or the time at which to perform a cleaning process, dependent on an actual or expected demand for beverages, or dependent on a target time for beverage retrieval. Shared resources may be applied to the production of beverages for high priority orders, while partially completed beverages for lower priority orders are staged for subsequent advancement.