Scheduling model for a small hospital

I work for a small hospital with 80 beds providing 24/7 care. I need your help to come up with an optimal scheduling model. This is not an ongoing project. What I need are the full-time staffing requirements for at least two models of staffing, one that runs on 8 hour shifts, the other on 12 hour shifts. In the end, I need to be able to present to upper management that these are the minimum requirements for staffing, including the number of Full Time Equivalents for each model. I may need to discuss further modifications, such as accounting for unanticipated sick days or injuries, but for now the assumption would be perfect employees who showed up for work reliable, never got sick or injured, etc. I need to be able to present the rational behind the model.