Operating Room

The hospital has to allocate a certain amount of operating room(OR) time to specific cardiac
procedures. Since the actual procedure time in the OR is random andwill - in the best of all cases
- vary around the expected procedure time, some procedures willexceed the forecasted durations
while others will be completed ahead of schedule. If the hospitalreserves too much time to a case,
the OR is likely to incur excessive idle time. If, however, thehospital reserves too little time to a
case, the hospital is likely to face schedule over-runs anddecreased service quality.

Case	Reserved Time (min)	Actual Time (min)	A/F Ratio
A	90	122	1.35
B	100	83	.83
C	120	121	1.01
D	150	145	.97
E	180	209	1.16

There is a new case, say, F. The reservation system predicts theoperating time to be 110 minutes.
From past experience, the doctors think that the reservation systemhas a certain percentage of
predicting errors (see the table for the data from previous 5cases).

The doctors wonder if Newsvendor model would help in theirplanning.

a) Construct an empirical distribution (discrete distribution) foroperating time of case F based
on the historical data.

b) If the doctors want to make sure that the reserved time isenough for the procedure with at
least 80% of the chance, how much time should be reserved for caseF? (Hint: First decide
what corresponds to “demand” and what corresponds to “orderquantity” in this OR context.
Then apply the appropriate service level formula.)

c) Given the reserved time in part b), what is the expectedovertime for case F? (Hint: overtime
happens when the procedure time exceeds the reservationduration.)

d) Given the reserved time in part b), what is the expected idletime for case F? (Hint: idle time
happens when the procedure time is less than the reservationduration.)