The assigning of new arrivals at a hospital emergency department to treatment rooms was examined. New patients are summarily triaged and assigned to a treatment room based on severity of their symptoms, the grade of a treatment room, and an exponential benefit curve that encourages the solver to schedule the most severe cases early. SAS’s OPTMODEL modeling language was employed to build the model and SAS’s MILP solver was used to perform the scheduling. Up to thirty patients were optimally assigned to depict the example of a large emergency department.