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IE $4820/6820$ Fall $2023$

Lab $2$

Due: Tuesday, November $21($at $11$:$59$pm$!)$

$($Complete this assignment in teams of two!$)$

Problem $1$: $($Inspired by Exercise $4\mathrm{.}9)$

In the Tie$-$Dye T$-$Shirt model, the owner is expecting the business to grow during the summer season. The

owner is interested in estimating the average time to produce an order and the utilization of the workers if

the arrival rate for orders increases. Re$-$run the model for $30$ eight$-$hour days with the arrival rate increased

by $20,40,60,$ and $80$ percent. Will the system have trouble meeting the demand? Perform your simulation

runs in Process Analyzer, reporting on system time, shirtmaker utilization, and packager utilization. Use

the statistics provided in Process Analyzer to justify your conclusions.

Problem $2$: $($Inspired by Exercise $4\mathrm{.}22)$

As part of a diabetes prevention program, a clinic is considering setting up a screening service in a local

mall. They are considering two designs: Design A: After waiting in a single line, each walk$-$in patient is

served by one of three available nurses. Each nurse has their own booth, where the patient is first asked

some medical health questions, then the patient$$s blood pressure and vitals are taken, finally, a glucose

test is performed to check for diabetes. In this design, each nurse performs the tasks in sequence for the

patient. If the glucose test indicates a chance of diabetes, the patient is sent to a separate clerk to schedule

a follow$-$up at the clinic. If the test is not positive, then the patient departs.

Design B: After waiting in a single line, each walk$-$in is served in order by a clerk who takes the patient$$s

health information, a nurse who takes the patient$$s blood pressure and vitals, and another nurse who

performs the diabetes test. If the glucose test indicates a chance of diabetes, the patient is sent to a separate

clerk to schedule a follow$-$up at the clinic. If the test is not positive, then the patient departs. In this

configuration, there is no room for the patient to wait between the tasks; therefore, a patient who has had

their health information taken cannot move ahead unless the nurse taking the vital signs is available. Also,

a patient having their glucose tested must leave that station before the patient in blood pressure and vital

checking can move ahead.

Assume that there is an $8\%$ chance $($stream $11)$ that the glucose test will be positive. For design A$,$ the

time that it takes to have the paperwork completed, the vitals taken, and the glucose tested are all

lognormally distributed with means of $6\mathrm{.}5,6\mathrm{.}0,$ and $5\mathrm{.}5$ minutes respectively $($streams $12,13,14).$ They

all have a standard deviation of approximately $0\mathrm{.}5$ minutes. For design B$,$ because of the specialization of

the tasks, it is expected that the mean of the task times will decrease by $15\%.$

Assume that the mall opens at $10$ am and that the system operates until $8$ pm$.$ Patients arrive to the system

according to a Poisson process that has an average rate of $9\mathrm{.}5$ per hour for the entire day. During the time

from $10$ am to $12$ noon the arrivals are less than the overall arrival rate. From $10$ am to noon, the rate is

only $6$ per hour. From noon to $2$ pm$,$ the rate increases to $14$ per hour. From $2$ pm to $4$ pm the traffic

lightens up again, back to $6$ per hour. From $4$ pm to $6$ pm$,$ the rate is $12$ per hour and finally from $6$ pm to

$8$ pm$,$ the rate is $10$ per hour. Assume that the clinic is open from $10$ am to $8$ pm $(10$ hours each day$)$ and

that any patients in the clinic before $8$ pm are still served. The distribution used to model the time that it

takes to schedule a follow up visit is also lognormally distributed with mean $5\mathrm{.}0$ minutes and standard

deviation $1\mathrm{.}0$ minute $($stream $15).$

Make a statistically valid recommendation as to the best design based on the average system time of the

patients. We want to be $95\%$ confident of our recommendation to within $3$ minutes.

Additional Comments:

$1)$ You need to specify how the patient arrival rate changes across the day for different time

periods. You cannot specify a stream number for this type of arrivals...don$$t worry about this.

$2)$ Run the model until ALL patients have been served. $($You will need to create your arrivals

schedule such that no more patients arrive after $8$pm$.)$

$3)$ Recommend one screening service design based on the following performance measures:

a$.$ Average time in system $($as stated in the problem$)$

b$.$ Probability of greater than a five$-$minute wait

Arena automatically captures the total amount of waiting time for any entity. To find this in

$$Build Expression$$ you would look under $$Special Purpose Attributes $$ Times$$ and there you

can find the syntax for the total waiting time. Or you can create your own statistic.

$4)$ Conduct the Compare Means tests within Output Analyzer. Report the test results $($recommended

screening service$),$ as well as report the resulting half$-$width found on the Compare Means tests.

If you did not use a complete CRN $($common random numbers$)$ approach and instead used

independent samplin