final report operating room surgical team …ioe481/ioe481_past_reports/f9201.pdffinal report...

University of Michigan Hospitals

Operating Room Surgical Team Utilization Study.

Final Report

December 11, 1992

Management Systems Department

Industrial and Operations Engineering

481 Senior Design Project

University of Michigan Hospitals, Ann Arbor, MI.

• Nilesh Dayal

Jeff Havlicek

Craig Hoffman

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Table of Contents

1. Executive Summary .2

2. Introduction 3

3. Approach and Methodology 3

4. Results 5

5. Recommendations 6

Appendices 9

Executive Summary

This project was initiated by the client, anesthesiologist Dr. Timothy Rutter, in anattempt to inspect case load and utilization during the hours of 5:30 PM and 9:00 PM,Monday through Friday for the University of Michigan Operating Rooms. The objectiveswere to integrate the information from the Surgi-Server system to provide information andrecommendations to modify the number of surgical teams operating at evening hours fromMonday through Friday and to modify the distribution of allocated time for each service.

Our findings shown in the results section of this report indicate that the number ofsurgical teams is in excess of the case load during the aforementioned evening hours. Withthe assistance of our client, our recommendations for decreasing the number of surgicalteams by hour are:

Table 1. Number of Surgical Teams Recommended

Time: Monday Tuesday Wednesday Thursday Friday Average3:00PM 15 18 18 17 17 174:00 PM 15 16 15 14 14 14.85:00PM 9 11 12 11 10 10.66:00PM 5 8 7 9 8 7.47:00PM 4 5 4 5 6 4.88:00PM 3 5 3 3 4 3.69:00PM 1 3 3 2 3 2.4

We have also determined the utilization of scheduled time for the entire operatingroom and also for each day of week and service. This information, along with many otherproposed utilization studies is the basis for our recommendations on a more efficient methodof scheduling allocated time to the various services. Our actual findings are in the resultssection. Our proposals can be found in the recommendations section of this report, but aresummarized below:

Table 2. Each Service With a Room Will Be Allocated 2 Hours from 5:3OPM-7:3OPM

DayofWeek: M T W Th F

ServiceCARDIAC 1 1 1 1

GYN.NEURO. 1 1ORTHO. 1 1

OTOPLASTICS

SEC 1SGI 1

SONSTXSVA 1 1

THORACIC 1

2

Introduction

The University Hospital Operating Room has twenty-one operating rooms for usebetween the normal operating hours of 7:30 AM to 5:30 PM. Surgical services expresseddesire to extend normal operating hours in order to better serve their needs. In response tothese demands, operating rooms were approved for scheduled use during evening hours after5:30PM.

On September 8, 1992, nine operating rooms were approved for scheduled usebetween the hours of 5:30 PM and 9:00 PM, Monday through Friday. Twelve surgicalservices are allocated to operating rooms during this time period. See Table 3: Services withallocated rooms between 5:30 PM and 9:00 PM.

Table 3: Services with allocated rooms between 5:30 PM and 9:00 PM.

(

DayofWeek: M T W Th F

ServiceCARDIAC 1 2 1

GYN. 1 1NEURO. 1 1 1ORTHO. 1 1

OTO 1 2PLASTICS 1 1 1

SEC 1SGI 1SON 1STX 1SVA 1 1

THORACICUnallocated 4 2 5 2 8

RoomsTotal Rooms 9 9 9 9 9

There is a support team on duty for each operating room whether a surgery is beingperformed or not. There is concern that these teams are not being effectively utilized, nor arethe surgical services using their allocated time.

This report recommends the number of University Hospital Operating Rooms(Teams) that should be allocated during the hours of 5:30 PM and 9:00 PM, Monday throughFriday, and how these rooms should be allocated by surgical service.

Approach and Methodology

Operating Room (OR) data for each case is collected and entered into the operatingroom’s Surgi-server. This data was then down-loaded to a PC-compatible text file format.This information was analyzed using STATA, a statistical package, and other PC softwarepackages.

The utilization of the operating rooms is studied and analyzed from a two monthperiod, September 8, 1992 to November 8, 1992, Monday through Friday, between the hours

3

of 5:30 PM and 9:00 PM. Our analysis of case load by hour began at 3:00 PM to help predictthe number of teams to schedule between 5:30 PM and 9:00PM.

In general, total utilization as defined by the University of Michigan HospitalOperating Room is defined as follows:

All Cases Done in any 24 hr Period Monday-FridayTotal Utilization =

Allocated Block Time

In specific this report has two methods for determining a utilization value. If theutilization value is a value for the hospital’s utilization over the two months or a specific dayof the week over the two months, then the Utilization was calculated by:

Utilization = Total Elapsed Surgury Minutes within the defmed times and datesTotal Allocated Block Time Minutes within the defined times and dates

The elapsed surgery minutes is the difference between patient in time and patient outtime which is taken from the Surgi-Server information. Also note that this definition givescredit to utilization no matter if the patient was being operated on during the exact allocatedblock time or not. This is congruent with the guidelines given to us on a department memoby Dr. Rutter. This definition gives a good overall volume indicator of how much theoperating rooms are being used.

The second method of calculating utilization is used for specific services. Thisformula only counts the amount of work done during the daily allocated time. For example,if a service never did a case during their allocated hours, then their utilization would be zero.Furthermore, the surgery minutes used for a case were cut if the case ran before or after thewindow of block time. The definition for service-related utilization values is determined by:

Total Elapsed Surgury Minutes within the AllocatedBlock Times for defmed times and dates

Utthzation=Total Allocated Block Time Minutes of Scheduled Time withinthe same defined times as dates

The total allocated block time minutes is the total amount of minutes of allocatedteams. As an example, if 9 teams are allocated for 3 1/2 hours for 9 different Fridays, thenthe total allocated block time = 9 x 3.5 x 9 x 60 = 17, 010 minutes. This number would thenbe used to divide whatever numerator was calculated in that instance. The ratio is thepercentage that we call utilization. The target total utilization for the University HospitalOperating Room is 75%.

Average case load by day of week by hour, from 3:00PM to 9:00PM, is also studiedand analyzed for this two month time period. The average case load is the total number ofcases being performed at the hour on a day of week divided by the number of days. Forexample, we found 101 cases that were being performed at exactly 3:00PM on the eightMondays of the two month period. Therefore, the average is 10 1/8 = 12.6 Cases.

Percentage of time the scheduled number of teams would be able to cover the numberof cases on any day during the hours from 3:00PM to 9:00PM was calculated. The numberof cases for each week during a particular hour is assumed to follow a normal distribution.With this assumption, the percentage of time that the number of teams are able to cover the

4

case load can be calculated for a varying number of teams. This information is used todetermine the number of teams to schedule by choosing a number of teams with anacceptable level of risk. Furthermore, a range value above and below the mean giving a 95%Confidence interval was calculated. This indicates that 95% of the time the number of casesbeing performed at a given time period will fall within the interval. For example, the 95%confidence interval for Monday - 3:00PM is 10.8 to 14.4. This means that 95 % of the timethere will be between 13 and 17 cases being performed at. 2.5% there will be less than 13cases and 2.5% of the time there will be more than 17 cases. This confidence interval wasused to determine an exact number of rooms(teams) to be scheduled for each time period.

A simulation model of the University Hospital Operating Rooms was also built tosimulate the activity of the Operating Room for each day of the week from the data from thetwo month period. A flexible, user-friendly simulation model was built in GPSS/H for easymodification in the future. The model calculated the total utilization as defined by theUniversity Hospital Operating Rooms by day of week; by number of total rooms open(Allocated rooms + Unallocated rooms). Please see Appendix L for the simulationassumptions and results along with the GPS S/H model file.

The results from the simulation could be used to recornniend the number of roomsthat should be allocated between 5:30PM and 9:00PM. Since many assumptions were madeto create this model, our recommendations do not use this information. It stills stands,however, as a excellent foundation for future studies.

Results

The results are displayed in graphical format in Appendices A - J. All the utilizationand case load calculations are averages over the entire two month period from September 8,1992 to November 8, 1992.

The day period is from 7:30AM to 5:30PM everyday of the week, Monday throughFriday, except for Thursday which is from 8:30AM to 5:30PM. Utilization calculations forThursdays account for the one hour difference. The evening period is from 5:30PM to9:00PM everyday of the week, Monday through Friday.

The following is a summary of the results:

Appendix A: Total Utilization - The total utilization of the day and evening periods.The total utilization is calculated using a 27 minute per case factor for turn around time togive an overall utilization of the operating rooms. It is also calculated using no factor of turnaround time.

Appendix B: Total Utilization By Service - The total utilization by surgical service ofthe day and evening periods during their allocated hours.

Appendix C: Average Case Load by Day of Week - The average case load by day ofweek, Monday through Friday, from 3:00PM to 9:00PM.

Avpendix D: Worksheet of Percentage of Time Scheduled Teams Will Cover CaseLoad By Hour - Worksheets of the percent chance that the number of teams schedule willcover the case load by hour, from 3:00PM to 9:00PM.

Appendix E: Total and Theoretical Utilization by Service - The total utilization bysurgical service for the evening period and the theoretical utilization by surgical service.Theoretical utilization represents the utilization by varying the allocated block time from 3hours (5:3OPM-8:3OPM) to 1 hour (5:3OPM-6:3OPM).

5

Appendix F: Average and Theoretical Utilization for Monday - The averageutilization for Monday by surgical service and the theoretical utilization. Theoreticalutilization represents the utilization by varying the allocated block time from 3 hours(5:3OPM-8:3OPM) to 1.5 hours (5:3OPM-7:OOPM).

Appendix G: Average and Theoretical Utilization for Tuesday - The averageutilization for Tuesday by surgical service and the theoretical utilization. Theoreticalutilization represents the utilization by varying the allocated block time from 3 hours(5:3OPM-8 :3OPM) to 1.5 hours (5:3OPM-7 :OOPM).

Appendix H: Average and Theoretical Utilization for Wednesday - The averageutilization for Wednesday by surgical service and the theoretical utilization. Theoreticalutilization represents the utilization by varying the allocated block time from 3 hours(5:3OPM-8:3OPM) to 1.5 hours (5:3OPM-7:0OPM).

Appendix I: Average and Theoretical Utilization for Thursday - The averageutilization for Thursday by surgical service and the theoretical utilization. Theoreticalutilization represents the utilization by varying the allocated block time from 3 hours(5 :30PM-8 :3OPM) to 1.5 hours (5:3OPM-7 :O0PM).

Appendix J: Average and Theoretical Utilization for Friday - The average utilizationfor Friday by surgical service and the theoretical utilization. Theoretical utilizationrepresents the utilization by varying the allocated block time from 3 hours (5:3OPM-8:3OPM)to 1.5 hours (5:3OPM-7:OOPM).

These results were used to determine the number of rooms to schedule from 5:30PMto 9:00PM, Monday through Friday, and how these rooms should be allocated by surgicalservice.

Recommendations

Our first recommendation concerns the number of rooms(teams) to schedule. Werecommend the following table:

Table 4. Number of Surgical Teams Recommended

Day: Monday Tuesday Wednesday Thursday Friday Average

Time: Teams Risk Teams Risk Teams Risk Teams Risk Teams Risk Teams3:00PM 15 18% 18 17% 18 18% 17 19% 17 15% 174:00PM 15 8% 16 12% 15 17% 14 22% 14 17% 14.85:00PM 9 16% 11 21% 12 23% 11 16% 10 21% 10.66:00 PM 5 23% 8 20% 7 25% 9 17% 8 18% 7.47:00 PM 4 23% 5 27% 4 23% 5 12% 6 19% 4.88:00PM 3 12% 5 14% 3 31% 3 23% 4 14% 3.69:00 PM 1 34% 3 20% 3 21% 2 30% 3 22% 2.4

Our recommendations are based on case load by hour data. This data can be found inAppendix C. This data shows that the current number of scheduled rooms(teams) exceedsthe case load for all time periods (3:00PM - 9:00PM) on every day of the week. The abovetable contains the recommended number of rooms to be scheduled for each hour from

6

3:00PM until 9:00PM for each day of the week. Our selection of the number of surgicalteams to staff was calculated by the following formula:

Recommended Teams = ROUND(.t + C.I. I + CjjOp (.i. + I C.I. I))

where, .t average case loadI C. I. I = absolute value of ± range which allows 95% Confidence IntervalCL! OP = percentage of time a room cannot host a patientROUND( ) = rounding to the nearest integer

This formula was developed to give a conservative recommendation of the number ofsurgical rooms (teams). This formula uses the 95% C.I. interval and then adds a factor thattries to compensate for the times when a room is not yet prepared for a new patient. A valueof 1/12 was assumed and used in the percentage of time a room cannot host a patient.

In addition, the table also inicates the average of the week for each hour (3:00PM to9:00PM). If it is more desirable to have the same number of rooms (teams) scheduled eachday for a specified time period, then the weekly average number of rooms(teams) should bescheduled. However, to accommodate this, an attempt must be made to more evenlydistribute the case load. For example, if 17 rooms (teams) are scheduled weekly at, 3:00PMbut the average case load on Wednesday is 18, then each service should attempt to shift someof this volume to the day with an average case load that is less than 17 (like Monday). Wefeel that reducing the number of rooms (teams) will be more cost effective while still beingable to effectively handle all the cases that enter the OR during these late hours.

Secondly, we recommend that allocated block between 5:30PM and 9:00PM besignificantly reduced. This recommendation is based on the fact that the utilization of thisallocated time is very low (as seen in Appendices A and B). From September 8, 1992 toNovember 8, 1992 the utilization of the 5:30PM to 9:00PM block is only 38.18%. Reductionof evening hour allocated block time should be accomplished in two ways: 1) by reducingthe evening hour time period from 3.5 hours to 2 hours, and 2) by limiting the number ofservices that are allocated time. Our recommended schedule for the evening hours is listed inTable 5. We found a two hour block of allocating time would increase many of the service’sutilization to a value near the 75% standard without creating any unrealistic, dangerouslyhigh values of service utilization. Please see Appendix E through J for more detail analysis.All block utilization times thar were roughly 75% or higher were recommended for thesenew evening allocation hours.

7

Table 5. Theoretical Utilizations of Each Service if Allocated 2 Hours from 5:3OPM-7:3OPM

Day of Week: M T W Th F

ServiceCARDIAC 108% 76% 95% 56% 132%

GYN. 0% 34% 13% 29% 26%NEURO. 46% 94% 25% 64% 84%ORTHO. 50% 51% 87% 129% 30%

OTO 47% 32% 62% 44% 68%PLASTICS 15% 23% 47% 13% 17%

SEC 43% 58% 17% 69% 88%SGI 34% 115% 45% 0% 67%

SON 0% 13% 12% 26% 25%STX 26% 34% 56% 23% 23%SVA 28% 117% 5% 90% 63%

THORACIC 40% 16% 68% 0% 73%

NOTE: The bold numbers indicate services which will be allocated block time of 2hours.

We would also like to recommend the following ideas for future developments. Costfactor analysis that investigates how percent risk affects cost will legitimize the optimal riskdecision when scheduling teams. A study on how much time is taken to clean and prepare aroom between patients would help to understand how much time is unavailable forutilization. More information gathering and analysis can be done to get a more realisticsimulation of the operating rooms. A task force could be established to develop ways thattypes of integrated information like that presented in this report could be made accessible andusable in every-day decision-making. Lastly, if this report proves to be a catalyst for change,then future teams should study how well these changes have been and what ways furtherimprovements can be made.

The project team would like to thank those people whose support made this report sosuccessful: Dr. Timothy Rutter, Liz Othman, Dr. Richard Coffey, Scott Lovelace, SheriDufek, and Regina Ritter.

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y

Day

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ay(7

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pm)

TB

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ve.

(5:3

Opm

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)

Tho

raci

cT

otal

Uti

liza

tion

111%

73%

C •— N •— n-N •—

100% 90%

80%

70%

60%

50%

40%

30%

20%

10% 0%

r:z:zzz:z

i•

66%

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Th%

II

—J

Mon

day

Tue

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pm)

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(5:3

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)

100% 90%

80%

70%

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50%

40%

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20%

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Uro

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Tota

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pm-9

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pm)

CIa

Ci.) E z

Mon

day

Ave

rage

Cas

eL

oad

22 20 18 16 14 12 10 8 6 4 2 0

3:00

4:00

5:00

6:00

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8:00

9:00

Tim

eof

Day

(PM

)

c-) © z

Tue

sday

Ave

rage

Cas

eL

oad

22 20 18 16 14 12 10 8 6 4 2 0

3:00

4:00

5:00

6:00

7:00

8:00

9:00

Tim

eof

Day

(PM

)

20

c,1

8

16 14

C12

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2 0

Wed

nes

day

Ave

rage

Cas

eL

oad

22

3:00

4:00

5:00

6:00

7:00

8:00

9:00

Tim

eof

Day

(PM

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c-) E z

Thu

rsda

yA

vera

geC

ase

Loa

d

22 20 18 16 14 12 10 8 6 4 2 0

IA

vera

geC

ase

Load

Number

ofTe

ams

H3:

004:

005:

006:

007:

008:

009:

00

Tim

eof

Day

(PM

)

Fri

day

Ave

rage

Cas

eL

oad

6:00

Tim

eof

Day

(PM

)

-I C E z

22 20 18 16 14 12 10 8 6 4 2 0

EEZ]

-I•1

•

3:00

4:00

5:00

H7:

008:

009:

00

Appendix DWorksheet of Percentage of Time Scheduled Teams

Will Cover Case Load By Hour

1011i’D

131415161718

19

20

21

Case Load at 3:00pm

Monday Tuesday Wednesday Thursday Friday

Week 1Week 2Week 3Week 4Week 5Week 6Week 7Week 8Week 9Mean

± at 95% C.I.

S

14 18 17 10 12

11 16 13 20 12

11 16 9 11 11

18 18 13 12 11

11 18 16 17 12

10 16 16 14 20

14 14 10 16 19

12 11 21 13 11

15 16 15 11

12.6 15.8 14.6 14.2 13.2

—‘1.8 1.5 2.4 2.1 2.4

Percentage of Time that Scheduled Teams will cover Case Load

i6,ei-t# of Teams Monday Tuesday Wednesday Thursday Friday

.6

C

0

C

15.8% 0.6% 11.0% 9.0% 18.5%

26.7% 1.8% 16.9% 15.3% 26.8%

40.6% 4.9% 24.6% 24.1% 36.7%

55.7% 11.1% 33.8% 34.9% 47.5%

70.0% 21.8% 44.1% 47.2% 58.6%

81.8% 36.6% 54.8% 59.7% 68.9%

90.2% 53.9% 65.1% 71.4% 78.0%

95.3% 70.4% 74.5% 81.1% 85.3%

98.0% 83.5% 82.3% 88.5% 90.8%

99.3% 92.1% 88.4% 93.5% 94.6%

99.8% 96.8% 92.9% 96.7% 97.0%

99.9% 98.9% 95.9% 98.4% 98.5%

Case Load at 4:00pm

Monday Tuesday Wednesday Thursday FridayWeek 1Week 2Week 3Week 4Week 5Week 6Week 7Week 8Week 9Mean

±at95%C.I.

# of Teams101112131415161718192021

16 17 13 8 911 12 13 15 1113 14 7 5 914 11 13 9 511 17 12 13 1211 10 13 16 1512 13 6 13 1712 9 17 11 7

11 12 12 712.5 12.7 11.8 11.3 10.21.2 1.9 2.2 2.3 2.6


Monday Tuesday Wednesday Thursday Friday7.9% 17.7% 29.8% 35.2% 47.7%19.9% 28.1% 40.8% 46.2% 57.8%38.9% 40.8% 52.6% 57.6% 67.4%61.1% 54.6% 64.3% 68.3% 76.0%80.1% 67.9% 74.7% 77.7% 83.2%92.1% 79.2% 83.2% 85.3% 88.8%97.6% 87.7% 89.7% 90.9% 92.9%99.4% 93.4% 94.1% 94.7% 95.8%99.9% 96.8% 96.9% 97.2% 97.6%100.0% 98.6% 98.5% 98.6% 98.7%100.0% 99.5% 99.3% 99.3% 99.4%100.0% 99.8% 99.7% 99.7% 99.7%

Week 1Week 2Week 3Week 4Week 5Week 6Week 7Week 8Week 9Mean

± at 95% C.I.

Case Load at 5:00pm

# of Teams34567891011121314

Monday Tuesday Wednesday Thursday Friday

C

Monday Tuesday Wednesday Thursday Friday10 13 14 5 67 8 13 13 88 11 7 3 115 8 10 5 64 11 9 9 88 9 5 10 128 10 4 8 107 8 11 8 3

8 12 10 47.1 9.6 9.4 7.9 7.61.3 1.2 2.3 2.0 2.0


1.4%4.9%13.0%27.5%47.4%67.9%84.0%93.6%98.0%99.5%99.9%100.0%

0.0%0.1%0.6%2.5%7.9%19.5%37.9%59.7%78.8%91.2%97.1%99.3%

3.3%6.0%10.2%16.3%24.3%34.0%45.0%56.3%67.1%76.7%84.5%90.3%

5.7%10.5%17.6%27.1%38.7%51.4%64.0%75.2%84.2%90.8%95.0%97.6%

7.0%12.5%20.4%30.7%42.9%55.7%68.0%78.6%86.8%92.5%96.1%98.2%

Case Load at 6:00pm


±at95% C.I.

# of Teams123456789101112

5 9 7 6 55 6 8 5 74 7 7 1 74 9 6 5 72 5 3 6 74 3 4 6 85 7 3 8 85 6 8 7 2

2 5 12 34.3 6.0 5.7 6.2 6.00.7 1.6 1.3 1.9 1.4


Monday Tuesday Wednesday Thursday Friday0.1% 1.9% 1.0% 3.6% 1.1%1.5% 4.8% 3.3% 7.3% 3.3%

11.4% 10.5% 9.1% 13.4% 8.4%40.5% 20.2% 20.2% 22.2% 17.9%76.6% 33.8% 36.9% 33.7% 32.3%95.5% 50.0% 56.6% 47.0% 50.0%99.6% 66.2% 74.8% 60.6% 67.7%100.0% 79.8% 87.8% 73.0% 82.1%100.0% 89.5% 95.2% 83.0% 91.6%100.0% 95.2% 98.5% 90.3% 96.7%100.0% 98.1% 99.6% 95.0% 98.9%100.0% 99.4% 99.9% 97.7% 99.7%

Week 1Week 2Week 3Week 4Week5Week6Week 7Week 8Week 9Mean

± at 95% C.I.

Case Load at 7:00pm

Monday Tuesday Wednesday Thursday Friday5 5 4 5 44 4 4 4 54 4 4 2 73 7 2 1 12 5 2 3 43 3 1 3 72 3 2 5 53 4 5 4 2

2 3 4 13.3 4.1 3.0 3.4 4.00.7 0.9 0.9 0.9 1.5


Monday Tuesday Wednesday Thursday Friday1.5% 1.6% 6.5% 3.3% 9.5%

11.4% 7.3% 22.5% 13.9% 19.1%40.5% 22.2% 50.0% 36.9% 33.1%76.6% 47.0% 77.5% 66.2% 50.0%95.5% 73.0% 93.5% 87.8% 66.9%99.6% 90.3% 98.8% 97.2% 80.9%100.0% 97.7% 99.9% 99.6% 90.5%

# of Teams1234

67

C

Case Load at 8:00pm


±at95% C.I.

# of Teams12ft

4567

1 2 4 3 33 5 2 4 23 6 2 1 50 5 2 1 12 3 1 2 22 2 1 1 42 2 1 1 30 1 4 1 1

2 4 4 11.6 3.1 2.3 2.0 2.40.8 1.2 0.9 0.9 0.9


Monday Tuesday Wednesday Thursday Friday29.9% 11.6% 15.7% 22.5% 15.5%62.4% 26.4% 40.1% 50.0% 37.7%87.6% 47.5% 69.3% 77.5% 65.2%97.7% 69.3% 89.6% 93.5% 86.3%99.8% 85.8% 97.8% 98.8% 96.4%100.0% 94.9% 99.7% 99.9% 99.4%100.0% 98.6% 100.0% 100.0% 99.9%

Case Load at 9:00pm


±at95%C.I.

# of Teams1234

0 2 3 3 32 3 1 2 20 2 0 0 30 4 2 1 11 1 1 2 00 1 2 1 42 1 2 0 30 2 4 0 0

3 3 3 1

0.6 2.1 2.0 1.3 1.90.6 0.7 0.8 0.8 0.9


Monday Tuesday Wednesday Thursday Friday65.9% 14.6% 20.7% 39.3% 27.0%93.3% 45.8% 50.0% 70.7% 53.0%99.5% 80.0% 79.3% 91.3% 77.8%100.0% 96.3% 94.9% 98.5% 92.7%

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Appendix FAverage and Theoretical Utilization for Monday

The Theoretical Utilizations were calculated bydividing total elapsed time by theoretical allocated time.Theoretical allocated time varied from 3 hours(5:3Opm-8:30pm) to 1.5 hours(5:3Opm-7:OOpm).

Ave

rage

Uti

liza

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(5:3

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100% 90%

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120%

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(5:3

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150%

140%

130%

120%

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7%

0 •— •— •—

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140%

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120%

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100% 90%

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70%

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10% 0%

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oret

ical

Uti

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Tue

sday

(5:3

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3%

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156%

•— •— •—

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100% 90%

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540

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nesd

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120%

110%

100% 90%

80%

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The

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Uti

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for

Wed

nesd

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126%

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Introduction

A simulation model of the University Hospital Operating Rooms was written inGPS S/H simulation language. The following are the assumptions and results of thesimulation. This information is included in this report as reference for future simulationprojects of the University Hospital Operating Room. These results were not directly usedto determine the recommendations of this report.

Simulation Model Assumptions

DATA

The data from the two month period is assumed to be a good indication of theutilization during the entire year. Therefore, the data was analyzed to determine thedistribution of arrival times, service times, and emergency cases. There are four mainassumptions concerning these distributions:

1) Patient inter-arrival distributions can be modeled as exponential distributions.

The patient inter-arrival distributions were determined from histograms based ontwo main breakdowns of the data: day of the week, and hour of the day. Only thehistograms based on day of the week showed a significant difference in inter-arrival distributions. These distributions resembled exponential distributions.Exponential distributions seem reasonable because it is modeling the inter-arrivaltimes of patients at a hospital. The arrival time of each patient is largelyindependent of the patient before since many of the patients are emergency cases,and these cannot be scheduled. Independent arrivals are usually well-modeled bythe exponential distribution. Please see Table 2: Exponentially distributed arrivalmeans by day of week.

The inter arrival distribution was assumed to remain constant during the entireperiod from 3:00pm to 9:00pm. This was based on analysis of the histograms thatwere based on a breakdown by hour of the day. These histograms were notsignificantly different from each other.

Day of the Week Inter-arrival means(minutes)

MONDAY 29.40TUESDAY 44.53NEDNESDAY 41.44THURSDAY 42.18FRIDAY 38.94

C.

Table 2: Exponentially distributed arrival means by day of week

2) The probability of a case requiring a specific service is constant.

This assumption was based on the fact that the number of data points from the twomonth period was insufficient to find an accurate distribution of arrivals bysurgical service.

The percentage of each service type was determined by adding up the number ofindividual cases for each service type and dividing by the total number of cases inour data set for arrivals between 3:00pm and 9:00pm. Since the number ofscheduled rooms changes for each day of the week, the percentage of service typewas figured for each day of the week. Please see Table 3: Probability ofSurgical Service by Day of the Week.

Table 3: Probability of Surgical Service by Day of the Week.

3) Service time distributions can be modeled as exponential distributions.

Histograms were produced for each type of service and it was found that eachservice time followed an exponential distribution. Since there were not enoughdata points in our 3:00pm to 9:00pm data set, we determined these distributionsfrom the entire set of data collected at all times of the day. Thus, it was assumedthat the service time for each type of service would not vary based on time of theday the surgery began.

The mean service times were found to be significantly different between emergentand non-emergent cases of the same surgical service, so separate mean times werecalculated. Please see Table 4: Mean service times by Surgical Service.

C

C

C

Service MONDAY TUESDAY WEDNESDAY HURSDAY FRIDAY

PLASTICS .050 .052 .109 .040 .016SEC .125 .086 .031 .140 .161DTO .125 .034 .125 .060 .145SGI .025 .103 .031 .000 .097SON .000 .052 .078 .080 .032SVA .025 .069 .031 .080 .065THORACIC .025 .017 .094 .000 .065ORTHO .200 .172 .172 .200 .113CARDIAC .100 .052 .078 .060 .097STX .075 .034 .063 .060 .065NEURO .075 .121 .047 .020 .0323YN .000 .086 .031 .120 .081)THER .175 .121 .109 .140 .032Sum 1 .000 1 .000 1.000 1 .000 1.000

4) The probability of a case being emergent is constant.

The data on emergent cases from 3:00pm to 9:00pm was found to be too scarce todetermine distributions by service, therefore a constant percentage of 32.9% wasused to determine the probability that a case was emergent. This was calculatedby counting the number of emergent cases and dividing by total cases from thedata collected between 3:00pm and 9:00pm.

Service Type Non-emergent Emergent(minutes) (minutes)

PLASTiCS 134.54 106.50SEC 152.91 146.89OTO 109.80 148.57SGI 247.75 1 23.43SON 105.20 223.75SVA 145.38 173.29

THORACIC 195.80 208.50ORTHO 128.19 150.00

CARDIAC 210.14 233.14STX 133.71 234.89

NEURO 155.00 231.71GYN 95.43 123.00

OTHER 1 29.96 241 .43

Table 4: Mean service times by Surgical Service

Detailed calculations of how well the data fits an exponential distribution isbeyond the scope of this project. The probability of a specific case, emergent or non-emergent, was fixed because it was not possible to find a distribution by day of week byservice type. Further analysis should be performed to determine how well the populationdata follows the exponential distribution, and to verify these results.

MODEL

The simulation model is set-up to simulate each day of the week, with the userhaving the ability to vary the number of unallocated rooms to have available. Thenumber of unallocated rooms on a given day of week is dependent upon the number ofallocated rooms (Please see Table 1: Services with allocated rooms between 5:30pm and9:00pm). The maximum number of total rooms that can be opened is nine, since thereare nine rooms currently open during 5:30pm to 9:00pm. The user may not change howthe rooms are allocated, i.e. the values from Table 1, but the model is created for simplemodifications to accomplish this.

When a patient arrives, based on the distribution of the day of week (Please seeTable 2: Exponentially distributed arrival means by day of week), the patient is assigneda case, which is based on the probabilities from Table 3: Probability of Surgical Serviceby Day of the Week. The service time for the case is also assigned. This is based on thevalues from Table 4: Mean service times by Surgical Service, which depends if the case

is emergent or non-emergent. The model sends 32.9% of the cases to the emergent casesegment of the model to capture an operating room.

Emergent cases first attempt to capture an unallocated room. If there are noneavailable it attempts to capture any open allocated room. If an emergent case arrives at atime when no rooms are available, unallocated rooms or allocated rooms, realisticallyanother operating room is opened up, and an on-call surgical staff is called in. Ourutilization figure depends only on the rooms (teams) that are normally available for use.Thus, even though some emergent cases are assigned a room, the model does not includethe use of this additional room that had to be opened because of an emergent case. Themodel terminates such cases, since they do not affect the utilization of the rooms V

available for normal use.

Non-emergent cases attempt to capture the surgical service’s allocated room. If itis in use or there is no room allocated to that service on a given day, then the caseattempts to capture an unallocated room. If all the unallocated rooms are in use, then thecase must wait for a room.

GPSS/H standard numerical attributes and transaction parameters are used tocalculate the maximum number of cases that waited, the average time a case waited, theutilization of the Operating Room as defined by the University Hospital, for eachsimulation run by day of week.

Simulation ResultsV V

From the simulation model, results were obtained indicating the maximum (number of cases waiting for a room in the six hour period, the average time that a casehad to wait for a room, and the total utilization as defined by the Hospital OperatingRoom.

Chart 1: Maximum Number of Cases Waiting, displays the maximum number ofcases that were waiting in the OR during the six hour simulation period. The maximumnumber of cases that waited is broken down first by day, and within each day by numberof rooms available. This graph shows that as the number of available rooms increases,the maximum number of cases that were waiting decreases. Adding more rooms willshorten the queue lines for rooms. (Please see Chart 1)

Chart 1: Maximum Number of Cases Waiting

4

3.5

3

1.5

zi

0.5

0

6789 89 56789 89 23456789Mon Tue Wed Thur Fri

Total Number of Rooms

Chart 2: Average Wait Time by Number of Rooms, displays the average time thateach case waited to be serviced. Again, this is broken down by day and by number ofavailable rooms. Similar to Chart 1, Chart 2 shows that as the number of rooms availableincreases, the average time that a case waited decreases. Again, with more roomsavailable, the smaller the queue and the shorter the time spent in the queue. (Please seeChart 2)

120

,100

40

2O

0

Chart 2: Average Wait Time by Number of Rooms

6 89Mon Tue Wed Thur


23456 789Fri

Finally, Chart 3: Utilization by Number of Rooms, displays the Utilization of the

OR, again broken down by day and by number of available rooms. This chart shows that

as the number of available rooms increases the utilization of the OR increases as well.

This may seem odd, however, it can be explained by examining the definition ofutilization as determined by the University Hospital. In the utilization equation the

denominator is a constant over the entire day because the number of allocated rooms is

constant for each day (e.g. Monday 5 allocated rooms, Tuesday 7 allocated rooms, etc.).However, as the number of rooms available increases, the number of cases performedincreases and the total service time increases. With an increasing numerator and constantdenominator, the utilization increases, in some cases beyond 100%.

6789 89 56789 89Mon Tue Wed Thur


250Chart 3: Utilization by Number of Rooms

200

C

150N

100

50

0

C

C

23456789Fri

SIMULATE Hospital Operating Rooms* Base Time Unit: 1 Minute*

**********************************************************************

* This model simulates the University of Michigan Hospital Operating *

* Rooms between 3pm and 9pm, Monday through Friday. *

* The arrival rates, service times, probability of the a specific *

* surgery, and the probability of the case being an emergency are *

* based on real data collected between 3pm and 9pm from September 8, *

* 1992 to November 8, 1992 *

**********************************************************************

*

* File Definition Control Statements *

******* ****** *********************************************************

*

MONDAY FILEDEF ‘monday.dic’TUESDAY FILEDEF ‘tuesda.dic’WEDNESDA FILEDEF ‘wednesd.d±c’THURSDAY FILEDEF ‘thursda.dic’FRIDAY FILEDEF ‘friday.dic’

*

********************************************* *************************

* Ampervariables and SYN and EQU Statements *

*

INTEGER &REPLY, &NTJMS , &NUMASR.MS, & IREAL &NTJNWAIT, &AVEWAIT, &UTIL, &NUMCASE

*

MON SYN 1TUE SYN 2WED SYN 3THUR SYN 4FRI SYN 5OTHER SYN 13PLASTICS EQU l,S,QSEC EQU 2,S,QOTO EQU 3,S,QSGI EQU 4,S,QSON EQU 5,S,QSVA EQU 6,S,QTHORCIC EQU 7,S,QORTHO EQU 8,S,QCARDIAC EQU 9,S,QSTX EQU 1O,S,QNEURO EQU 11,S,QGYN EQU 12,S,Q

*

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* Function Control Statements *

**********************************************************************

* Mean arrival time for each day - exponentially distributedARRIVALS FUNCTION &REPLY,D5

MON,29.40/TUE,44.53/WED,41.44/THUR,42.18/FRI,38.94

* Probability of a specific surgery as a function of day of weekCASE FUNCTION &REPLY,E5MON, FN(MONCASE) /TUE,FN(TUECASE) /WED,FN(WEDCASE) /THUR, FN(THURCASE) /FRI, FN(FRICASE)

* Probability by case for MondayMONCASE FUNCTION RN2,D11.050,PLASTICS/.175,SEC/.300,OTO/.325,SGI/.350,SVA/.375,THOpCIC/.575, ORTHO/ .675, CARDIAC! .750, STX/ . 825,NEURO/1, OTHER

* Probability by case for TuesdayTUECASE FUNCTION RN3,D13.052,PLASTICS/.138,SEC/.172,OTO/.276,SGI/.328,SON/.397,SVA/.414,THORAC:.586, ORTHOJ .638, CARDIAC! .672, STX/ .793 ,NEURO/ .879, GYN/1, OTHER

* Probability by case for WednesdayWEDCASE FUNCTION RN4,D13.109,PLASTICS/.141,SEC/.266,OTO/.297,SGI/.375,sON/.406,SvA/.500,THORAC:.672,ORTHO/.750,CARDIAC/.813,STX/.859,NEURO/.891,GYN/l,OTHER

* Probability by case for ThursdayTHURCASE FUNCTION RN5,Dll.040,PLASTICS/.180,SEC/.240,OTO/.320,SON/.400,SVA/_.600,ORTHO/.660,CARDIAC/.720,STX/.740,NEURO/.860,GYN/l,OTHER

* Probability by case for FridayFRICASE FUNCTION RN6,D13.016,PLASTICS/.l77,SEC/.323,OTO/.419,SGI/.452,SON/.516,SVA/.581,THORAC.694, ORTHO/ .790, CARDIAC! .855, STX/ .887 ,NEURO/ .968, GTh/1, OTHER

* Mean of service times by surgical service for non-emergent casesNONECASE FUNCTION PF1,D13PLASTICS, 134. 54/SEC, 152. 91/OTO, 109. 80/SGI, 247.75/SON, 105. 2/SVA, 145. 38/_THORACIC, 195. 80/ORTHO, 128.19/CARDIAC, 210. 14/STX, 133. 71/NEURO, 155. 00/GYI’OTHER, 129.96

* Mean of service times by surgical service for emergent casesECASE FUNCTION PF1,D13PLASTICS, 106.5/SEC1146. 89/OTO, 148. 57/SGI, 123.43/SON, 223 .75/SVA, 173 .29/_THORACIC,208.50/ORTHO,150.00/CARDIAC,233.14/sTx,234.89/NEURO,231.71/_GYN, 123.00/OTHER, 241.43

* Table Control Statements *

**********************************************************************

*

QTEAMS QTABLE ROOMS,0,10,5 Residence time table for* queue: ROOMS**********************************************************************

* Model Segment 1 *

*******************************************************************

*

GENERATE RVEXPO(7,FN(ARRIVALS)) ,,,,,1PF, 1PL Cases arrive*

NEWCASE ASSIGN 1;FN(CASE),PFTRANSFER .329, ,EMERGENTASSIGN l,FN(NONECASE) ,PL

*

UNASROOMGETUNROM

QUEUEENTERQUEUEDEPARTDEPARTADVANCELEAVEDEPARTTRANSFER

TEST GEQUEUE

UNAS SRMROOMSYSTEMUNAS SRMROOMSRVEXPO(9,PL1)ROOMSYSTEM,KILL

Assign a surgical serviceSee if emergent caseAssign service time

See if the service’s roomis being used, if not

enter the room, otherwisesee if there is an availunassigned roomSystem is used to findtotal utilization

Exponentially dist servtime

* Model Segment 2 (Run-Control Blocks) *

**********************************************************************

*

*

*

360 Model is for one 6 hour day 3-9pm

TERMINATE 1 End the Xact-movement phase

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* Run-Control Statements *

**********************************************************************

*

UNLIST CSECHO don’t echo control statements

TEST NETEST G

GETROOMQUEUEENTERQUEUEDEPARTDEPARTADVANCELEAVEDEPARTTRANSFER

PF1, OTHER, GETUNROMR(PF1) ,0,UNASROOM

QUEUE ROOMSPF1PF1SYSTEMPF1ROOMSRVEXPO(8,PL1)PF1SYSTEM, KILL

Q(PF1),Q(UNASSRM),GETROOM See which line is shorte:ROOMS the assigned room queue

the unassigned room queueSystem is used to find totaltotal utilization

Exponentially dist serv timetime

Emergent case arrives,find an avail unassignedroom, if not capture an

avail assigned room* NOTE: IF NO OPEN ROOM

XACT IS KILLED- -

SEE REPORT FOR DETAILS.

*

EMERGENT ASSIGN 1,FN(ECASE),PLTEST G R(ROOM),0,FINDRMTRANSFER ,GETUNROM

FINDRM SELECT E 1PF,l,12,0,R,GETROOMEKILL TERMINATE 0KILL TERMINATE 0

*

*

*

GENERATE

MENU PUTPIC LINES = 14

0

OPTION MENU

1 Simulate for Monday2 Simulate for Tuesday3 Simulate for Wednesday4 Simulate for Thursday5 Simulate for Friday6 End session

AGAIN1 PUTSTRING (‘ Enter an option number’)PUTSTRING (‘ ?‘)

*

GETLIST ERR=MESSAGE1, &REPLY*

IF (&REPLY<1)OR(&REPLY>6)_OR(FIX(&REPLY) ‘NE’&REPLY)

*

MESSAGE1 PUTSTRING (‘OBad selection; Please try again ‘)GOTO AGAIN1

*

ENDIF*

********************************************************************

*

IF &REPLY=1 Simulate for MONDAY*

AGAIN2 PUTSTRING (‘OEnter # of unassigned rooms available’)PUTSTRING (‘ (Choose an integer from 1 to 4) ‘)PUTSTRING (‘ ?‘)GETLIST ERR=MESSAGE2, &NUNRMS

*

IF (&NUMRNS<1)OR(&NUMRMS>4)_OR(FIX(&NtIMRNS) ‘NE’&NUMRMS)

MESSAGE2 PUTSTRING (‘OBad entry; Try again ‘)GOTO AGAIN2

*

ENDIF

PUTSTRING (‘0 The simulation program is running*

CLEAR*

ROOM STOR.GE &NUNRMSPLASTICS STORAGE 1 Room allocation for MONDAYSEC STORAGE 1OTO STORAGE 0SGI STORAGE 0SON STORAGE 0SVA STORAGE 1

THORACIC STORAGE 0ORTHO STORAGE 0CARDIAC STORAGE ISTX STORAGE 0NEURO STORAGE 1.GYN STORAGE 0

*

LET &NUMASRNS=5*

LET &NUMWAIT=0 Reinitialize vars to 0LET &AVEWAIT=0LET &UTIL=0LET &NUMCASE=0* Reset random number generatcRMULT 1000001200000,300000,400000,500000,600000,700000,800000,900000*

DO &I=1,50,1 Repeat simulation 50 timesCLEARSTART 1. Perform the simulation*

LET &NDNWAIT=QM(ROOMS)+&NUMWAIT Store calculationsLET &AVEWAIT=QX(ROOMS)+&AVEWAITLET &UTIL= (QC(SYSTEM) *QT(SYSTEM) )+&UTILLET &Nt3MCASE=N(NEWCASE) -N(EKILL) ÷&NUMCASE*

ENDDO*

PUTPIC FILE=MONDAY, LINES=6, (&NTJThjNS+&NTJMASRMS,&NUMCASE/50 ,&NUMWAIT/50,&AVEWAIT/50, ((&UTILI5O)I(360*&NTJMASRMS))*100)

0 MONDAY: ** Total RoomsAve Number of cases performed =

Maximum number of cases waited =

Average wait = ***.**

Total utilization = ***.** 9 (Total utilization defined 1

*

**********************************************************************

*

ELSEIF &REPLY=2 Simulate for TUESDAYAGAIN3 PUTSTRING (‘OEnter of unassigned rooms available’)

PUTSTRING (‘ (Choose an integer from 1 or 2) ‘)PUTSTRING (‘ ?‘)GETLIST ERR=MESSAGE3 , &NTJMRNS

*

IF (&NtThrRNS<1)OR(&NUNRMS>2)OR(FIX(&NUMS) ‘NE’&NUMRMS)


*

ENDIFPUTSTRING (‘0 The simulation program is ruxining

*

CLEAR*

ROOM STORAGE &NUZMSPLASTICS STORAGE 1 Room allocation for TUESDAY CSEC STORAGE 0OTO STORAGE 0SGI STORAGE 1SON STORAGE 0SVA STORAGE 0THORACIC STORAGE 0ORTHO STORAGE 1CARDIAC STORAGE 2STX STORAGE 0NEURO STORAGE 1GYN STORAGE 1

*

LET &NUMASRNS=7*

LET &NUMWAIT=0 Reinitialize vars to 0LET &AVEWAIT=0LET &UTIL=0LET &NUNCASE=0* Reset random number generatoRMULT 100000, 200000, 300000, 400000, 500000, 600000, 700000, 800000, 900000*

DO &I=1,50,1 Repeat simulation 50 timesCLEARSTART 1 Perform the simulationLET &NUMWAIT=QM(ROOMS)+&NUMWAIT Store calculationsLET &AVEWAIT=QX(ROOMS)+&AVEWAITLET &UTIL= (QC(SYSTEM) *QT(SYSTEM) )÷&UTILLET &NUMCASE=N (NEWCASE) -N (EKILL) +&NUMCASEENDDO*

PUTPIC FILE=TUESDAY,LINES=6, (&NUNS+&NUMASRMS, &NUMCASE/50 ,&NUMWAIT/50&AVEWAIT/50, ((&UTIL/50)/(360*&NUMASP.NS))*100)

0 TUESDAY: ** Total RoomsAve Number of cases performed =



Total utilization = 9 (Total utilization defined b’

*

**********************************************************************

*

ELSEIF &REPLY=3 Simulate for WEDNESDAY*

AGAIN4 PUTSTRING (‘OEnter # of unassigned rooms available’)PUTSTRING (‘ (Choose an integer from 1 to 5) ‘)PUTSTRING (‘ ?‘)GETLIST ERR=MESSAGE4, &NUNS

*

IF (&NUNRMS<1)OR(&Nuh1iN5>5)_OR(FIX(&NMS)’NE’&NTThtRNS)


*

ENDIF

PUTSTRING (‘0 The simulation program is running 1)

*

CLEAR*

ROOM STORAGE &NUMPNSPLASTICS STORAGE 1 Room allocation for WEDNEDAYSEC STORAGE 0OTO STORAGE 1SGI STORAGE 0SON STORAGE 0SVA STORAGE 0THORACIC STORAGE 0ORTHO STORAGE 1CARDIAC STORAGE 0STX STORAGE 1NEURO STORAGE 0GYN STORAGE 0

*

LET &NUMASRNS=4*

LET &NtINWAIT=0 Reinitialize vars to 0LET &AVEWAIT=0LET &UTIL=0LET &NUMCASE=0* Reset random number generatRMt3LT4 l00000,200000,300000,400000,500000,600000,700000,800000,90000C

DO &I=1,50,1 Repeat simulation 50 timesCLEARSTART 1 Perform the simulationLET &NUMWAIT=QM(ROOMS)÷&NtTMWAIT Store calculationsLET &AVEWAIT=QX(ROOMS) +&AVEWAITLET &UTIL=(QC(SYSTEM) *QT(SYSTEM) )+&UTILLET &NUMCASE=N(NEWCASE) -N(EKILL) +&NtJNCASEENDDO*

PUTPIC FILE=WEDNESDA,LINES=6, (&NUMRNS+&Nt1MASRNS, &NtIMCASE/50, &NUMAIT/5O,&AVEWAIT/50, ((&UTIL/50)/(360*&NUMASRNS))*100)

0 WEDNESDAY: ** Total RoomsAve Number of cases performed =



Total utilization = 9 (Total utilization defined I

*

**********************************************************************

*

ELSEIF &REPLY=4 Simulate for THURSDAY*

AGAIN5 PUTSTRING (‘OEnter of unassigned rooms available’)PUTSTRING (‘ (Choose an integer from 1 to 2) ‘)

PUTSTRING (‘ ?‘)GETLIST ERR=MESSAGE5,&NUMRNS

*

IF (&Nt7MRMS<1)OR(&NtJMRMS>2)_OR(FIX(&NtJMRMS) ‘NE’&NUNS)


*

ENDIF

PUTSTRING (‘0 The simulation program is running*

CLEAR*

ROOM STORAGE &NOPISPLASTICS STORAGE 0 Room allocation for THURSDAYSEC STORAGE 0OTO STORAGE 2SGI STORAGE 0SON STORAGE 1SVA STORAGE 1THORACIC STORAGE 0ORTHO STORAGE 0CARDIAC STORAGE 1STX STORAGE 0NEURO STORAGE I.GYN STORAGE 1

*

LET &NUMASRMS=7*

LET &NOMWAIT=0 Reinitialize vars to 0LET &AVEWAIT=0LET &UTIL=0LET &NUMCASE=0* Reset random number generatoRMULT 100000,200000,300000,400000,500000,600000,700000,800000,900000*

DO &I=1,50,1 Repeat simulation 50 timesCLEARSTART 1 Perform the simulationLET &NUMWAIT=QM(ROOMS)+&NtTMWAIT Store calculationsLET &AVEWAIT=QX (ROOMS) +&AVEWAITLET &UTIL= (QC(SYSTEM) *QT(SYSTEM) )+&UTILLET &NUMCASE=N(NEWCASE) -N(EKILL) +&NDMCASEENDDO*

PUTPIC FILE=THURSDAY,LINES=6, (&NtmS+&ASRMs,&NuNCASE/50,&NuMcAIT/50,&AVEWAIT/50, ((&UTIL/50) / (360*&NUMASRNS)) *100)

0 THURSDAY: ** Total RoomsAve Number of cases performed ***•**

Maximum number of cases waitedAverage wait ***.**

Total utilization 9 (Total utilization defin S

*

****** ****************************************************************

*

ELSEIF &REPIjY=5 Simulate for FRIDAY*

AGAIN6 PUTSTRING (‘OEnter # of unassigned rooms available’)PUTSTRING (‘ (Choose an integer from 1 to 8) ‘)PUTSTRING (‘ ?‘)GETLIST ERR=MESSAGE6, &NOMRMS

*

IF (&N.MS<1)OR(&NU.MS>8)OR(FIX(&NUNBNS) ‘NE’&NtTh.MS)


*

ENDIFPUTSTRING (‘0 The simulation program is running

*

CLEAR*

ROOM STORAGE &NtThIRMSPLASTICS STORAGE 0 Room allocation for FRIDAY

SEC STORAGE 0OTO STORAGE 0SGI STORAGE 0SON STORAGE 0SVA STORAGE 0THORACIC STORAGE 1ORTHO STORAGE 0CARDIAC STORAGE 0STX STORAGE 0NEURO STORAGE 0GYN STORAGE 0

*

LET &NtJMASRMS=1*

LET &NDMWAIT=O Reinitialize vars to 0LET &AVEWAIT=0LET &tTTIL=0LET &NUMCASE=O* Reset random number generato

RMtJLT 100000,200000,300000,400000,500000,600000,700000,800000,900000*

DO &I=l,50,1 Repeat simulation 50 timesCLEARSTART 1 Perform the simulationLET &NUMWAIT=QM(ROOMS)+&NTJMWAIT Store calculationsLET &AVEWAIT=QX (ROOMS) +&AVEWAITLET &UTIL= (QC(SYSTEM) *QT(SYST) ) +&UTILLET &NTJMCASE=N(NEWCASE) -N(EKILL) +&NUNCASEEN’DDO*

PUTPIC FILE=FRIDAY,LINES=6, (&Nt3MRMS÷&NtYMASRNS,&NUMCASE/50,&NUMWAIT/50,_&AVEWAIT/50,((&UTIL/50)/(350*&NtTMASp.Mg))*100)

o FRIDAY: ** Total RoomsAve Number of cases performed = CMaximum number of cases waited =

Average wait =

Total utilization = % (Total utilization defined I

*

*

ELSEGOTO DONEENDIF

*

PUTSTRING (‘0 End of simulation! ‘)*

GOTO MENUDONE PUTSTRING (‘0 Bye! ‘)

END

* C

‘nr’:r

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