Health insurance providers are clamping down on how much they’ll pay for emergency services, and the hospital is considering replacing some physicians with physician assistants (PAs). Registration will not change, except to send patients to a PA, as opposed to an M.D. Assume that the PA takes 5 minutes to determine that a patient should exit with a prescription and 10.5 minutes either to refer the patient to hospital admissions or to refer the patient to the M.D. for completion of the diagnosis. On average, 65% of patients leave the PA with a prescription, 5% are referred to hospital admissions, and the remainder sees the M.D. For those patients seeing the M.D., 83% leave with a prescription after 10 minutes, and the remainder are referred to hospital admissions after 60 minutes with the M.D. Patients spend, on average, 32 minutes in line in the PA examination area, and those that see an M.D. spend an average of 20 minutes in the line in the M.D. exam area.

1. On average, how long does a patient stay at each step in the ER process?
2. How long does the average patient stay in the ER process in total (be careful because some patients leave early)?
3. How many patients at each step in the ER process? In total?
4. How many Registration Clerks, PAs and Doctors need to be in each resource pools (consider the utilization rates of each resource pool)? Hint: Assume utilization rates close to 75-80% are reasonable.
5. If Registration Clerks cost $40,000 per year, PAs cost $60,000 per year and Doctors cost $150,000 per year, is the process change cost-effective?
6. How will the process change affect the time and number of customers in the system? Will the customer experience improve?