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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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ASSIGN OR BLOCKS TO OR-DAYOUTPUT

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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

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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

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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

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CONCLUSIONS & FUTURE RESEARCH

Questions?j.t.vanessen@utwente.nl