optimize or−schedule to reduce number of required beds theresia van essen, joël bosch
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OPTIMIZE OR−SCHEDULE TO REDUCE NUMBER OF REQUIRED BEDSTheresia van Essen, Joël Bosch
Optimize OR-Schedule to Reduce Number of Required Beds
Reduce number of required beds:
Less admissions
Reduce length of stay
Level bed utilization
9-11-2011 2/26
CONTEXT
Optimize OR-Schedule to Reduce Number of Required Beds 9-11-2011 3/26
BED UTILIZATION
Patient LOS Option 1 Option 2
1 3 Monday Tuesday
2 3 Tuesday Wednesday
3 2 Thursday Wednesday
Optimize OR-Schedule to Reduce Number of Required Beds 9-11-2011 4/26
BED UTILIZATION
Mon
day
Tuesd
ay
Wed
nesd
ay
Thurs
day
Friday
0
1
2
3
Option 1
Patient LOS Option 1 Option 2
1 3 Monday Tuesday
2 3 Tuesday Wednesday
3 2 Thursday Wednesday
Optimize OR-Schedule to Reduce Number of Required Beds 9-11-2011 5/26
BED UTILIZATION
Mon
day
Tuesd
ay
Wed
nesd
ay
Thurs
day
Friday
0
1
2
3
Option 1
Patient LOS Option 1 Option 2
1 3 Monday Tuesday
2 3 Tuesday Wednesday
3 2 Thursday Wednesday
Optimize OR-Schedule to Reduce Number of Required Beds 9-11-2011 6/26
BED UTILIZATION
Mon
day
Tuesd
ay
Wed
nesd
ay
Thurs
day
Friday
0
1
2
3
Option 1
Patient LOS Option 1 Option 2
1 3 Monday Tuesday
2 3 Tuesday Wednesday
3 2 Thursday Wednesday
Optimize OR-Schedule to Reduce Number of Required Beds 9-11-2011 7/26
BED UTILIZATION
Mon
day
Tuesd
ay
Wed
nesd
ay
Thurs
day
Friday
0
1
2
3
Option 1Option 2
Patient LOS Option 1 Option 2
1 3 Monday Tuesday
2 3 Tuesday Wednesday
3 2 Thursday Wednesday
Optimize OR-Schedule to Reduce Number of Required Beds
Beliën and Demeulemeester (2007)
Stochastic length of stay
Optimization
Minimize sum required beds
Van Oostrum et al. (2008)
Mean length of stay
Optimization
Vanberkel et al. (2011)
Stochastic length of stay
Evaluation
9-11-2011 8/26
RELEVANT LITERATURE
Optimize OR-Schedule to Reduce Number of Required Beds
Generate OR blocks
Maximize OR utilization
Satisfy overtime probability
Assign OR blocks to OR-day
Minimize number beds
Satisfy OR availability
Satisfy surgeon availability
Satisfy capacity instrument sets
9-11-2011 9/26
MODEL
Optimize OR-Schedule to Reduce Number of Required Beds
Blocks are assigned to one specialist
Maximize sum of expected duration
Sum expected duration plus slack is less than capacity
Solve with Column Generation
9-11-2011 10/26
GENERATE OR BLOCKS
08:00 16:00
Optimize OR-Schedule to Reduce Number of Required Beds
Planning horizon
Days with OR and surgeon availability
OR blocks
Number of patients of each type
Required instruments
Probability distribution LOS
9-11-2011 11/26
ASSIGN OR BLOCKS TO OR-DAYINPUT
LOS 1 2 3 4 5
Probability 0.10 0.30 0.40 0.15 0.05
Optimize OR-Schedule to Reduce Number of Required Beds 9-11-2011 12/26
ASSIGN OR BLOCKS TO OR-DAYDISTRIBUTION BEDS
23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 530
20
40
60
80
100
Number beds
Pro
ba
bili
ty1
0.8
0.6
0.4
0.2
Optimize OR-Schedule to Reduce Number of Required Beds
Simulated Annealing
Swap two OR blocks from two different days
If swap is feasible, determine number required beds
Better solution: accept
Worse solution: accept with probability
9-11-2011 13/26
ASSIGN OR BLOCKS TO OR-DAYMODEL
Te
Optimize OR-Schedule to Reduce Number of Required Beds 9-11-2011 14/26
ASSIGN OR BLOCKS TO OR-DAYMODEL
OR 1 OR 2
Day 1 1 2
Day 2 3 4
Mon
day
Tuesd
ay
Wed
nesd
ay
Thurs
day
Friday
Satur
day
Sunda
y0
2
4
6
8
10
Nu
mb
er
Be
ds
Optimize OR-Schedule to Reduce Number of Required Beds 9-11-2011 15/26
ASSIGN OR BLOCKS TO OR-DAYMODEL
OR 1 OR 2
Day 1 4 2
Day 2 3 1
Mon
day
Tuesd
ay
Wed
nesd
ay
Thurs
day
Friday
Satur
day
Sunda
y0
2
4
6
8
10
Nu
mb
er
Be
ds
Optimize OR-Schedule to Reduce Number of Required Beds
Assignment of OR blocks to OR-days
Number required beds per day
9-11-2011 16/26
ASSIGN OR BLOCKS TO OR-DAYOUTPUT
Optimize OR-Schedule to Reduce Number of Required Beds 9-11-2011 17/26
RESULT HAGAZIEKENHUISORTHOPEDICS
1/11
/201
0
3/11
/201
0
5/11
/201
0
7/11
/201
0
9/11
/201
0
11/1
1/20
10
13/1
1/20
10
15/1
1/20
10
17/1
1/20
10
19/1
1/20
10
21/1
1/20
10
23/1
1/20
10
25/1
1/20
10
27/1
1/20
1020
25
30
35
40
45
50
Original Schedule
Nu
mb
er
Be
ds
Optimize OR-Schedule to Reduce Number of Required Beds 9-11-2011 18/26
RESULT HAGAZIEKENHUISORTHOPEDICS
1/11
/201
0
3/11
/201
0
5/11
/201
0
7/11
/201
0
9/11
/201
0
11/1
1/20
10
13/1
1/20
10
15/1
1/20
10
17/1
1/20
10
19/1
1/20
10
21/1
1/20
10
23/1
1/20
10
25/1
1/20
10
27/1
1/20
1020
25
30
35
40
45
50
Minimize Beds
Original Schedule
Nu
mb
er
Be
ds
Optimize OR-Schedule to Reduce Number of Required Beds 9-11-2011 19/26
RESULT HAGAZIEKENHUISORTHOPEDICS
1/11
/201
0
3/11
/201
0
5/11
/201
0
7/11
/201
0
9/11
/201
0
11/1
1/20
10
13/1
1/20
10
15/1
1/20
10
17/1
1/20
10
19/1
1/20
10
21/1
1/20
10
23/1
1/20
10
25/1
1/20
10
27/1
1/20
1020
25
30
35
40
45
50
Max OR Utilization
Minimize Beds
Original Schedule
Nu
mb
er
Be
ds
Optimize OR-Schedule to Reduce Number of Required Beds
Applicable to surgical wards
Applicable to nonsurgical wards
No OR blocks, but individual patients
Emergency patients can be incorporated
Add distribution of emergency patients per day
9-11-2011 20/26
APPLICATIONS
Optimize OR-Schedule to Reduce Number of Required Beds
Number beds can be reduced
Even when OR utilization increases
Costs can be reduced
Information for nurse rostering provided
Develop iterative approach
Close wards during weekend
9-11-2011 21/26
CONCLUSIONS & FUTURE RESEARCH