EGRM $6681$ Simulation Techniques and Applications

Industrial and Systems Engineering & Engineering Management

UNIVERSITY OF NEW HAVEN

Workshop #$2$a February $5,2024$

Jobs arrive at a shop, following a Poisson distribution with a mean rate of six every one$-$half hour.

Each job requires an operation on a special machine. The operation time is approximated by an

exponential distribution with a mean of $12$ minutes. There are three identical machines that could

be used for jobs. Assume there is enough room for parts to wait for their turn of the operation.

Make any assumption$($s$)$ necessary to answer the following questions.

$1.$ Develop a simulation model of this shop with ARENA and run it for $1$ hours to get estimates

of the average wait time in the queue, average number in the queue, utilization of the machines,

and the count of completed jobs.

$2.$ The new requirement is that no new jobs are accepted at the end of the working day and all

jobs that arrived before the end of the shift are completed before the shut down of the shift.

Implement this new requirement in your model developed in $(1)$ and note the changes in output.

$3.$ Animate the Resource $($s$)$ for a more enhanced visual of this operation.

$4.$ We are told that the jobs coming to the shop are from two sources, each having their own

arrival rate and distribution. Specifically, Jobs from customer A have a mean arrival rate of $4$

per hour following the Poisson distribution while Customer B$$s jobs arrive with the mean inter$-$

arrival time of $7\mathrm{.}5$ minutes following the exponential distribution. Implement this new

information and determine the count of completed jobs for both customers.

$5.$ Repeat step #$15$ times where you run the model for $5,10,50,100$ and $500$ hours. Compare

the various measures of performance $($say the server utilization, average time and maximum in

the queue, and average and maximum number in the queue$)$ for each run length. Look at yhe

Measures in a tabular form as well as graphically and discuss what you observe and whether

you may be able to generalize your finding in any way$).$ Do this part at home and submit your

findings in a $1-$page report by coming Sunday evening.