Name: Lucero Vargas

Name: Lucero Vargas

Professor: Dr. Parisay

Due Date: February 2, 2010 Updated: Jan 2011

Parisay’s comments are in red.

Parisay’s results were different from Vargas’s result. However, the general idea of analysis is important. My comment is based on Vargas’s output.

1- Consider the following system. Create an Arena model. Create a Word file to contain the followings:

a) Problem statement as stated here

All times are in minutes. Parts called AA arrive to a section of our system and go through Station 1 for a process that takes Unif (3,5), . Then go to Station 2 for a process that takes Unif(1,3). Interarrvial time is distributed as expo(8). Other parts called BB arrive to this section of our system. It takes 5 minutes to be transferred to Station 1 for a process that takes Unif (3,5) . Then go to Station 2 for a process that takes Norm(3,0.5). Interarrvial time is distributed as expo(12).

After Station 2 all parts AA and BB may be sent to different route. About 60% of them are sent to Station 4 and then Station 5 and then leave for Warehouse Y. The rest of them, after Station 2, will be sent to Station 3 and then leave for Warehouse X.

The process at Station 1 requires 1 worker. The process at Station 2 requires 1 doctor and 2 nurses. The doctor takes 15 minutes break every 1 hour. The process at Station 3 requires 1 bed and it will take Trai(30,38,45) . The process at Station 4 requires 3 of tool X and 2 of tool Y and it will take Gama(2, 5) . The process at Station 5 requires 2 carts and it will take Erlang(2.5,2). Carts have failure with a pattern that follows expo(200) for up time and Unif(30,50) for down time. We have one of Station 1, one of Station 2, 3 identical Station 3, 3 parallel Station 4, and one of Station 5. Simulate for 10,000 min. We are also interested in the time parts (AA or BB) spend in system for those that leave from Warehouse X and for those that leave from Warehouse Y.

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b) Draw logical model using a software (past it into your Word file)

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c) Copy of statistical output (past it into your Word file)

ARENA Simulation Results

Vargas - License: STUDENT

Summary for Replication 1 of 1

Project: hw 4 Run execution date : 2/ 1/2010

Analyst: Vargas Model revision date: 1/31/2010

Replication ended at time : 10000.0 Minutes

Base Time Units: Minutes

TALLY VARIABLES

Identifier Average Half Width Minimum Maximum Observations

______

Record X 2222.6 (Corr) 42.429 9987.4 784

Record Y 2193.9 (Corr) 11.815 9984.7 1254

AA.VATime 30.125 .76649 9.3186 54.044 1213

AA.NVATime .00000 .00000 .00000 .00000 1213

AA.WaitTime 224.54 (Corr) .00000 782.16 1213

AA.TranTime .00000 .00000 .00000 .00000 1213

AA.OtherTime .00000 .00000 .00000 .00000 1213

AA.TotalTime 254.67 (Corr) 11.815 826.41 1213

BB.VATime 35.489 .86762 15.914 57.271 825

BB.NVATime .00000 .00000 .00000 .00000 825

BB.WaitTime 201.48 (Corr) .00000 780.44 825

BB.TranTime .00000 .00000 .00000 .00000 825

BB.OtherTime .00000 .00000 .00000 .00000 825

BB.TotalTime 236.97 (Corr) 18.040 831.26 825

Station 3.Queue.WaitingTime 463.59 (Corr) .00000 779.26 787

Station 4.Queue.WaitingTime .31767 .09740 .00000 10.494 1272

Station 5.Queue.WaitingTime 37.521 (Corr) .00000 168.17 1255

Station 1.Queue.WaitingTime 10.790 2.5295 .00000 55.792 2122

Station 2.Queue.WaitingTime 3.1519 .20315 .00000 15.556 2120

DISCRETE-CHANGE VARIABLES

Identifier Average Half Width Minimum Maximum Final Value

______

AA.WIP 32.835 (Corr) .00000 64.000 56.000

BB.WIP 20.479 (Corr) .00000 38.000 29.000

tool x.NumberBusy 3.8446 .20580 .00000 9.0000 9.0000

tool x.NumberScheduled 9.0000 (Insuf) 9.0000 9.0000 9.0000

tool x.Utilization .42719 .02287 .00000 1.0000 1.0000

tool y.NumberBusy 2.5631 .13720 .00000 6.0000 6.0000

tool y.NumberScheduled 6.0000 (Insuf) 6.0000 6.0000 6.0000

tool y.Utilization .42719 .02287 .00000 1.0000 1.0000

Doctor.NumberBusy .50613 .01948 .00000 1.0000 1.0000

Doctor.NumberScheduled .79387 (Insuf) .00000 1.0000 1.0000

Doctor.Utilization .50613 .01948 .00000 1.0000 1.0000

worker.NumberBusy .85116 (Corr) .00000 1.0000 1.0000

worker.NumberScheduled 1.0000 (Insuf) 1.0000 1.0000 1.0000

worker.Utilization .85116 (Corr) .00000 1.0000 1.0000

carts.NumberBusy 1.2928 .08318 .00000 2.0000 2.0000

carts.NumberScheduled 2.0000 (Insuf) 2.0000 2.0000 2.0000

carts.Utilization .64640 .04159 .00000 1.0000 1.0000

bed.NumberBusy 2.9615 (Corr) .00000 3.0000 3.0000

bed.NumberScheduled 3.0000 (Insuf) 3.0000 3.0000 3.0000

bed.Utilization .98718 (Corr) .00000 1.0000 1.0000

Nurses.NumberBusy 1.0122 .03895 .00000 2.0000 2.0000

Nurses.NumberScheduled 2.0000 (Insuf) 2.0000 2.0000 2.0000

Nurses.Utilization .50613 .01948 .00000 1.0000 1.0000

Station 3.Queue.NumberInQueue 38.872 (Corr) .00000 68.000 60.000 possible bottleneck, run for longer time, add plot

Station 4.Queue.NumberInQueue .04041 .01268 .00000 3.0000 .00000

Station 5.Queue.NumberInQueue 4.7690 (Corr) .00000 22.000 14.000

Station 1.Queue.NumberInQueue 2.2903 .64083 .00000 15.000 1.0000

Station 2.Queue.NumberInQueue .66833 (Corr) .00000 5.0000 1.0000

OUTPUTS

Identifier Value

______

AA.NumberIn 1269.0

AA.NumberOut 1213.0

BB.NumberIn 854.00

BB.NumberOut 825.00

tool x.NumberSeized 3816.0

tool x.ScheduledUtilization .42719

tool y.NumberSeized 2544.0

tool y.ScheduledUtilization .42719

Doctor.NumberSeized 2120.0

Doctor.ScheduledUtilization .63754

worker.NumberSeized 2122.0

worker.ScheduledUtilization .85116

carts.NumberSeized 2510.0

carts.ScheduledUtilization .64640

bed.NumberSeized 787.00

bed.ScheduledUtilization .98718

Nurses.NumberSeized 4240.0

Nurses.ScheduledUtilization .50613

System.NumberOut 2038.0

The values of Record X and Record Y seems unreasonable, but I could not find the mistake. I had 199.7 and 62.3. Also for total time AA and BB I had 113.3 and 118.2.

d)Create asummary table of major performance measures with acceptable ranges/values and your comments.

Minimum value is usually not important and we do not want to include in table. You need to specify a limit for acceptable Max, so just one number and not a range. Acceptable range is usually used for utilization.

Identifier / Average / Minimum / Maximum / Acceptable Values / Comments
Record X / 222.6 / 42.42 / 9987.4
Record Y / 2193.9 / 11.82 / 9984.7
AA Value Added Time / 30.13 / 9.32 / 54.04 / 35-50 / Needs to be increased
AA total Wait Time / 224.54 / 0 / 782.16 / 100-200 / Try to decrease, perhaps too many in queue
AA Total Time / 254.67 / 11.82 / 826.41 / 135-250 / Too high, need to reduce
BB Value Added Time / 35.49 / 15.91 / 57.27 / 40-55 / Lets try to increase here
BB Wait Time / 201.48 / 0 / 780.44 / 150-250 / Try to reduce here
BB Total Time / 236.97 / 18.04 / 831.26 / 190-300
Station 3 Queue Waiting Time / 463.59 / 0 / 779.26 / 200-300 / Too high
Station 4 Queue Waiting Time / 0.32 / 0 / 10.49 / Very good time here
Station 5 Queue Waiting Time / 37.52 / 0 / 168.17 / 2 / A little too high, needs to be looked into
Station 1 Queue Waiting Time / 10.79 / 0 / 55.79 / 15-30
Station 2 Queue Waiting Time / 3.15 / 0 / 15.56
AA WIP / 32.84 / 0 / 64 / 15-25 / Too much inventory need here
BB WIP / 20.48 / 0 / 38 / 10-20
Tool X Utilization / 0.43 / 0 / 1 / 0.85-0.95 / Under utilized!
Tool Y Utilization / 0.43 / 0 / 1 / 0.85-0.95 / Under utilized!
Doctor Utilization / 0.51 / 0 / 1 / 0.75-0.85 / Should be utilized a little more
Worker Utilization / 0.85 / 0 / 1 / 0.75-0.85 / Good work
Carts Utilization / 0.65 / 0 / 1 / 0.85-0.95 / Should be utilized a little more
Bed Utilization / 0.99 / 0 / 1 / 0.85-0.95 / Too high…will cause high wait time
Nurse Utilization / 0.51 / 0 / 1 / 0.75-0.85 / Too low, look into staggering shifts
Station 3 Number in Queue / 38.87 / 0 / 68 / 15-25 / Too many waiting
Station 4 Number in Queue / 0.04 / 0 / 3 / 1-5
Station 5 Number in Queue / 4.77 / 0 / 22 / 2-7
Station 1 Number in Queue / 2.29 / 0 / 15 / 1-5
Station 2 Number in Queue / 0.67 / 0 / 5 / 1-3

e)Plot number in line during simulation for Station 2 and Station 5 in the same chart.

Station 2 and Station 5

Conclusion: these stations should not create a problem as bottleneck. However the statistical output indicate a possible bottleneck at Station 3.

f) Write a report for a manager, using a simple language, explain the performance of this system.

Dear Manager,

After observing the area of the hospital that you had mentioned you were looking to improve, I have come to my final recommendations. I modeled the system in a computer software program called Arena 10.0.

The simulating your hospital identified utilization of different resources as in the table below.

Personnel / Utilization
Doctor Utilization / 0.51
Worker Utilization / 0.85
Nurse Utilization / 0.51

It is wrong to think that personnel should be working at anything over 85% because of laws and regulations that require personnel to take breaks and give allowances, but these numbers especially for the doctors and nurses appear to be very low. Perhaps staggering shifts of the nurses would increase their utilization, or offering some sort of work that could be done when they are not with patients could help increase their work time. Based on acceptable range of utilization, 0.75-0.85, the utilization of worker is fine, however, doctor and the two nurses are under-utilized, but we cannot reduce their number.

As for the equipment that you currently have in the hospital, this is what its utilization looks like:

Equipment / Utilization
Tool X Utilization / 0.43
Tool Y Utilization / 0.43
Carts Utilization / 0.65
Bed Utilization / 0.99

Because equipment doesn’t need breaks and allowances, there percentages should be higher than humans, but we should not insist it to be any higher than 95% either because we do have to take into consideration break downs and failures of the equipment. Based on acceptable range of utilization, 0.85-0.95, the utilization of Tools X and Y is too low. We can reduce number of these tools to 6 of X and 4 of Y. Then we can expect a utilization of 0.63 (3*0.43/2). This new utilization will still be low, however we cannot reduce it any more. Carts are also under-utilized, but we cannot reduce them. Beds are over-utilized. We can add one more bed and the expected utilization will be 0.74 (3*0.99/4). This new utilization will be low, however we had to accept it as if not we will face bottleneck at Station 3.

Another area that caught my eye was a few wait times that appeared to be quite high. The table below shows you which station, and what its average wait time is.

Station / Wait Time (mins)
Station 3 Queue Waiting Time / 463.59
Station 4 Queue Waiting Time / 0.32
Station 5 Queue Waiting Time / 37.52
Station 1 Queue Waiting Time / 10.79
Station 2 Queue Waiting Time / 3.15

Since some of these wait times are so high, they are causing lines to increase which could mean a higher cost in waiting space, and inventory for equipment. It could also mean less time that is spent dealing with the patients, which in turn reflects on your customer satisfaction. (Be specific and talk about Station 3.)

Hopefully this information is helpful in some ways. For ideas on implementing or finding suggestions to improve some of the numbers you see, I am here to help and offer more insight.

Thank you,

Lucero Vargas

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