MIME 5100
Final Exam
Due Wednesday, 4/30/2014, 5:00 PM
4/21/2014
On campus students: Please put your solution in a large envelop with your name on it and
bring it to my office (NI 4006D) in person between 3:00 PM to 5:00 PM on Wednesday,
4/30/2014, 5:00 PM. No solutions will be accepted before 3:00 PM or after 5:00 PM.
Students who do not have access to campus: please save solutions in PDF format and
Email by 5 PM on Wednesday, 4/30/2014.
This is a take-home exam. Open book, no time limit. Please sign the honor pledge: I
have not given or received any help in this exam. Name _____________________,
Signature ____________________
For the three problems below submit hardcopies of the following:
a) A write-up explaining the logic for developing your model and the steps that you
followed to develop this model.
b) A printout showing your Arena model.
c) The report from Arena. Export the report in a PDF or word file and print it.
d) A summary of observations are conclusions. This should include the steps that
you did to verify the model. Discuss how to improve the system performance.
e) Explain if the assumptions of the model are realistic, in your opinion.
1.
(40 pts) A company has developed a training program for a certain class of jobs.
There are three phases to the training program, phases 1, 2 and 3. Upon
completion of each phase, each trainee takes a test. If she passes the test, she
moves on to the next phase. If she fails, she must repeat that phase of the
program and retake the test. This procedure continues until the trainee passes the
tests for all three phases.
Let p be the probability that the trainee fails the test for the ith phase on the first
attempt. Let pn be the probability that the trainee fails the test on the nth attempt.
Each phase of instruction requires one week, before the test for that phase may be
taken. The duration of the instruction period remains the same regardless of the
times the trainee repeats the phase. These probabilities of a trainee failing the
first, second and third tests, are 𝑝1 = 0.4, 𝑝2 = 0.5, 𝑝3 = 0.2, respectively.
You can build an ARENA model, or use Excel to perform the simulation. You
should determine the number of replications required to estimate these quantities
with acceptable accuracy.
Perform a simulation to estimate the time, in weeks, for a trainee to complete the
training program. Estimate the mean time, and standard deviation, and make a
histogram of the time to complete the program.
2.
(20 points) In problem 1, the cost of each phase is $500 to the company, and the
cost of test for each phase is $75. These amounts are the same for each phase.
Estimate the mean cost and its standard deviation of completing the training per
employee.
3.
(40 points) A hospital has 100 beds available for occupancy. The interarrival time
of patients is exponential with a mean value of 0.2 days. This means that 5
patients arrive per day, on average. The duration of stay of a patient in the
hospital is also exponential with a mean value of 0.1 days. This means that if all
beds are occupied, then 10 patients are discharged the next day, on average. If
there are no available beds, no new patients are admitted until a bed becomes
available.
Construct an Arena model to simulate the hospital operations. Plot the time
history of the number of patients in the system
Run your model for 365 days. Terminate the simulation at the end of the 365th
day and ignore those patients who were in the system at the time. Study the
Arena report, and determine the following: a) The average number of beds
occupied, b) the probability of a patient being denied admission. Summarize the
observations and conclusions of the study.