Mini Case #4
Operating Room Scheduling & Capacity Management
A mid-size rural hospital had 10 operating rooms. It provided a whole host of surgical services,
being the only hospital for a large rural area. The ORs were staffed every day for 600 minutes
(10hrs) each. The hospital employed enough core staff to open up to 10 ORs on any given day.
The actual number of open ORs varied depending on the need (which depended on surgery
bookings) and staff availability (which varied due to vacations and time-off requests for
educational purposes). Surgeons were not employees of the hospital and billed directly for their
services. Virtually, all surgeons were assigned blocks. These were periods of guaranteed
OR-time allocations. Such allocations did not guarantee surgeons’ access to a particular OR.
The hospital had a centralized case scheduling station, where it scheduled cases one at a
time. Scheduled case lengths were recommended by a software that used the average of recent
similar cases performed by the surgeon. Surgeons could request more than the recommended
time, but not less, depending on patient characteristics.
Although many surgeons’ cases on any given day were scheduled back to back in a single OR,
it was not possible to schedule all cases in a single OR. This happened because some
surgeries required special equipment, which was available only in some ORs.
The hospital experienced both staffed OR idle time as well as overtime, often on the same
day. The VP of operations was concerned that ORs were not scheduled optimally. You are
tasked with helping the director of surgical operations answer the following specific questions.
(i)
Is the hospital doing a good job of estimating surgical case lengths?
a. The hospital is doing a pretty good job of estimating case lengths
(ii)
How many ORs are open on average during normal weekday business hours?
(iii)
What is the average and the standard deviation of the utilization of each OR during the
normal weekday business hours?
(iv)
What is the average weekday overtime usage for each OR?
(v)
Plot the distribution of scheduled start and close times of ORs? What does this plot tell
you about the current scheduling practices?
(vi)
Does the hospital open an optimal number of staffed ORs each weekday?
> # Q1. Is the hospital doing a good job of predicting case lengths?
Residual standard error: 44.31 on 9709 degrees of freedom
Multiple R^2: 0.6923, Adjusted R^2: 0.6922
F-statistic: 2.184e+04 on 1 and 9709 DF, p-value: < 2.2e-16
> # Let us try some other factors, e.g. weekday and room. Why?
Residual standard error: 42.22 on 9696 degrees of freedom
Multiple R-squared: 0.721, Adjusted R-squared: 0.7206
F-statistic: 1789 on 14 and 9696 DF, p-value: < 2.2e-16
> # How about case number?
Residual standard error: 42.15 on 9695 degrees of freedom
Multiple R-squared: 0.7219, Adjusted R-squared: 0.7215
F-statistic: 1678 on 15 and 9695 DF, p-value: < 2.2e-16
> # The improvements in R-sq in the last model are marginal
> # Q2. How many ORs are open each day?
Scheduled day of the week Avg no. of open rooms
1
1
8.42
2
2
8.12
3
3
8.56
4
4
8.03
5
5
8.21
> # Q3. Average and Standard Deviation of Room utilization
Room
Avg Util
SD
1
1
0.51
0.24
2
2
0.51
0.17
3
3
0.42
0.20
4
4
0.37
0.20
5
5
0.44
0.22
6
6
0.45
0.22
7
7
0.48
0.21
8
8
0.60
0.22
9
9
0.54
0.26
10
10
0.69
0.26
> # Q4. Overtime use
Room Avg Overtime
1
1
78.77
2
2
30.00
3
3
85.41
4
4
80.44
5
5
90.57
6
6
70.66
7
7
93.33
8
8
72.58
9
9
50.00
10
10
110.69
SD
49.36
NA
48.82
74.51
44.32
28.85
67.14
34.34
12.29
64.34
Q5
> # Q6.Optimal number of ORs?
>
> # Step 1: Find total minutes of demand by weekday
>
> # We first add up OR mins actual for each seqday and weekday
> # Plot total demand for a particular day of week (say Monday)
> # We see some outliers, but most data is scattered around the mean
> # Let us summarize demand for Monday
>
> summary(totormin$Demand[totormin$Weekday==1])
Min. 1st Qu. Median
Mean 3rd Qu. Max.
51 2287
2636 2583 3055 3956
> # Let us next find the mean and SD of demand for each Weekday
Weekday Demand
1
1 2582.52
2
2 2259.73
3
3 2585.82
4
4 2157.58
5
5 2277.36
> # Next, we find SD of total mins by weekday
Weekday
SD
1
1 728.73
2
2 548.99
3
3 553.66
4
4 585.48
5
5 550.39
> # Note that SD is about 25% of average demand, which is generally considered low variability
>
> # Plot empirical distribution
>