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 and will in the best of all cases- vary around the expected procedure time, some procedures will exceed the forecasted durations while others will be completed ahead of schedule. If the hospital reserves too much time to a case, the OR is likely to incur excessive idle time. If, however, the hospital reserves to little time to a case, the hospital is likely to face schedule over-runs and decreased service quality.

Case A:

Reserved Time: 90 min.

Actual Time: 122 min.

A/F Ratio: 1.35

Case B:

Reserved Time: 100 min.

Actual Time: 83 min.

A/F Ratio: .83

Case C:

Reserved Time: 120 min.

Actual Time: 121 min.

A/F Ratio: 1.01

Case D:

Reserved Time: 150 min.

Actual Time: 145 min.

A/F Ratio: .97

Case E:

Reserved Time: 180 min.

Actual Time: 209 min.

A/F Ratio: 1.16

There is a new case, say, F. The reservation system predicts the operating time to be 110 minutes. From past experiences, the doctors think that the reservation system has a certain percentage of predicting error (see table)

The doctors wonder if Newsvedor model would help in their planning. [Hint: Part A asks for the order quantity that meets the demand 80% of the time. Once you know the order quantity, you can compute other measures.]

a) If the doctors want to make sure that the reserved time is enough for the procedure with at least 80% of the chance, how much time should be reserves for case F?

b) What is the expected overtime for case F?

c) What is the expected idle time for case F?