A hospital emergency room is trying to plan holiday weekend staffing for a Saturday, Sunday, and Monday. Regular-time nurses can
A hospital emergency room is trying to plan holiday weekend staffing for a Saturday, Sunday, and Monday. Regular-time nurses can work any two days of the weekend at a rate of $300 per day. In general, a nurse can handle 10 patients during a shift. The demand is not known, however. If more patients arrive than the capacity of the regular-time nurses, they must work overtime at an average cost of $50 per patient overload. The Saturday demand also gives a good indicator of Sunday–Monday demand. More nurses can be called in for Sunday–Monday duty after Saturday demand is observed. The cost is $400 per day, however, in this case.
The hospital would like to minimize the expected cost of meeting demand.
Suppose that the following scenarios of 3-day demand are all equally likely:
(100,90,20), (100,110,120), (100,100,110), (90,100,110), (90,80,110), (90,90,100), (80,90,100), (80,70,100), and (80,80,90).