Homework 9
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School
Georgia Institute Of Technology *
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Course
6501
Subject
Industrial Engineering
Date
Dec 6, 2023
Type
Pages
4
Uploaded by ElderThunderSparrow15
Homework 9
Question 12.1
Describe a situation or problem from your job, everyday life,
current events, etc., for which a design of experiments approach
would be appropriate.
In my previous role, I worked as a data scientist for a large consumer fashion company. In my tenure, there were
many times that we would have ideas on how to best market our products or determine the sort order on the
website. In order for us to do that, we would implement A/B testing to see how each order or sort algorithm
performed. This would help the site merchandising team make decisions on which products to push and what
order they should be in.
Question 12.2
To determine the value of 10 different yes/no features to the
market value of a house (large yard, solar roof, etc.), a real estate
agent plans to survey 50 potential buyers, showing a fictitious
house with different combinations of features. To reduce the
survey size, the agent wants to show just 16 fictitious houses. Use
R’s FrF2 function (in the FrF2 package) to find a fractional factorial
design for this experiment: what set of features should each of the
16 fictitious houses have? Note: the output of FrF2 is “1” (include)
or “-1” (don’t include) for each feature.
features <- FrF2(16, 10)
features
## A B C D E F G H J K
## 1 -1 -1 -1 -1 1 1 1 1 -1 1
## 2 -1 -1 1 -1 1 -1 -1 1 1 -1
## 3 1 1 1 1 1 1 1 1 1 1
## 4 -1 -1 -1 1 1 1 1 -1 1 -1
## 5 1 -1 -1 1 -1 -1 1 1 1 1
## 6 1 1 -1 -1 1 -1 -1 -1 1 1
## 7 1 -1 -1 -1 -1 -1 1 -1 -1 -1
## 8 1 -1 1 1 -1 1 -1 1 -1 -1
## 9 1 1 1 -1 1 1 1 -1 -1 -1
## 10 -1 1 1 -1 -1 -1 1 1 -1 1
## 11 -1 1 -1 1 -1 1 -1 -1 -1 1
## 12 -1 -1 1 1 1 -1 -1 -1 -1 1
## 13 -1 1 1 1 -1 -1 1 -1 1 -1
## 14 1 1 -1 1 1 -1 -1 1 -1 -1
## 15 -1 1 -1 -1 -1 1 -1 1 1 -1
## 16 1 -1 1 -1 -1 1 -1 -1 1 1
## class=design, type= FrF2
Some of the features that we could include in this set based on my area (California) would be:
Pool
Solar
Backyard
Detached
Garage/Parking
Question 13.1
For each of the following distributions, give an example of data
that you would expect to follow this distribution (besides the
examples already discussed in class).
a. Binomial
When looking at sales data for the ordering of products that I talked about above, we could look at if the
customers bought or didn’t buy a certain product.
b. Geometric
Using the above example, we could look at the probability that someone will buy one of the two products.
c. Poisson
We could also measure the number of sales in a certain time frame - perhaps during black Friday from 12-
1am.
d. Exponential
Using the previous, we could also look at the time between orders and it would follow exponential
distribution.
e. Weibull
We could follow the time that it takes for a car to break down as we would expect the failure rate to increase
with time.
Question 13.2
In this problem you, can simulate a simplified airport security system at a busy airport. Passengers arrive
according to a Poisson distribution with λ1 = 5 per minute (i.e., mean interarrival rate ±1 = 0.2 minutes) to the
ID/boarding-pass check queue, where there are several servers who each have exponential service time with
mean rate ±2 = 0.75 minutes. [Hint: model them as one block that has more than one resource.] After that, the
passengers are assigned to the shortest of the several personal-check queues, where they go through the
personal scanner (time is uniformly distributed between 0.5 minutes and 1 minute). Use the Arena software (PC
users) or Python with SimPy (PC or Mac users) to build a simulation of the system, and then vary the number of
ID/boarding-pass checkers and personal-check queues to determine how many are needed to keep average wait
times below 15 minutes. [If you’re using SimPy, or if you have access to a non-student version of Arena, you can
use λ1 = 50 to simulate a busier airport.]
Arena Design
Unfortunately, I ran out of time to get this simulation to run without bottlenecking and exceeding the limit of entities
for the student version of Arena. That being said, I think it would have been possible to change some of the
settings so that I could run efficiently and within the 15 minute window per passenger with anywhere from five to
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