Question: Valley View Hospital faces somewhat seasonal demand. Patients defer elective surgery in the summer and in the holiday season at the end of the year. As a result, the forecast of patient days of demand is as follows (a patient day is one patient staying for one day in the hospital):
Fall Winter Spring Summer
Forecast 90,000 70,000 85,000 65,000
The hospital uses regular nurses, part-time nurses (when the hospital can get them), and contract nurses (who are not employees). Contract nurses work a number of hours which varies depending on their contract established with the hospital. Regular nurses are paid a sum of $15,500 per quarter for 60 days of work; part time nurses are paid $6500 per quarter for 30 days of work. Contract nurses get an average of $17,200 per quarter for 60 days of work. It costs $1000 to hire or lay off any of these three types of nurses. Suppose that regular nurses are set at a level of 800 nurses for the year. Each regular nurse works the equivalent of 60 days per quarter. The remainder of the demand is made up by 50 percent part-time and 50 percent contract nurses on a quarter-by-quarter basis. What is the cost of this plan starting at the beginning of Fall with a level of 800 regular nurses, 200 part-time nurses, and 200 contract nurses? Assume it takes 0.8 nurse day to provide around-the-clock care for each patient day.