Week9
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School
Georgia Institute Of Technology *
*We aren’t endorsed by this school
Course
6501
Subject
Industrial Engineering
Date
Dec 6, 2023
Type
Pages
15
Uploaded by BrigadierEnergyTapir20
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Week9
2023-10-24
#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.
#Answer: My previous job as a marketing analyst. A/B testing was very useful for me on digital marketing
platform. My company use shopify to sale grocery products. Every time we think of promotion events, we prefer
use A/B testing to test out what type of promotions will attract more customers to purchase. Evaluate how much
revenue we will make on each promotions, and how effective the customers would use the promotion code.
For instance, Halloween is coming. We need to create a promotion sale for candies. So first, we need to decide
the discount amount for different candies. And then, we need to create a least two different banner for our
website to promote the sales. The banners would have some small difference for customers such as same
wording with different fonts, different backgroup color, different graphics etc. We will run the promotion for at least
14 days. So we can test out which banner is more affective for the testing group of customers. When we collect
the data, we can use the best banner to promote our online sales for all customers.
#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.
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#install.packages("FrF2")
rm(list = ls())
library
(dplyr)
library
(FrF2)
library
(tidyverse)
library
(magrittr)
library
(tidyr)
library
(reshape2)
library
(kableExtra)
set.seed(12)
houses <- FrF2(
nruns=16, nfactors=10, factor.names = c(
'Back Yard', 'Pool', 'Front Yard', 'Driveway', 'Garage',
'3 Bedrooms', 'Washing Machine', 'Dish Washer', 'Basement', 'HOA'),
default.levels = c('1', '-1')
) %>% as_tibble() %>% rownames_to_column('House')
kable(houses)
HouseBack.YardPoolFront.YardDrivewayGarageX3.BedroomsWashing.MachineDish.WasherBasementHOA
1
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#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 - A single family house with a driveway or without a driveway.
b. Geometric - In a vaccination lab, how many times of failure on inventing a new vaccine will be seen until the
first success.
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c. Poisson - In a concert, the performing organizer may want to know the estimate time and audiences arrive
before the concert starts, and estimate time when audiences to leave. So the concert organizer will know
when will be the appropriate time to start the concert and let the audiences know when will be the last
encore.
d. Exponential - For example, suppose a big supermarket would have new customer arrive in store every 3
minutes. We want to measure the rate of this first customer get into the store, how long will take until the
next customer come in.
e. Weibull - Keep the high pitch sounds on until the glass breaks.
#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 interracial 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.]
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#import simpy and random libraries
#!pip install simpy
import
simpy as
sy
import
random
# set the number of variable and time limits.
random.seed(1)
num_queues = 24 # 24 queues
num_scanners = 18 # 18 scanners
runTime = 600
total_time = 0
total_passengers = 1
num_passengers = 500
class
Airport(object):
#ID/boarding pass check queue and security scanning
def
__init__(self, env, num_queues, num_scanners):
self.env = env
self.queue = sy.Resource(env, num_queues)
self.scanner = sy.Resource(env, num_scanners) #The ID check process. It takes a passenger, checks their ID,then passes the passeng
er to the next step.
def
IDcheck(self, passenger):
ID_service_time = random.expovariate(.75)
yield
self.env.timeout(ID_service_time) #Security Scan step. Passenergs are sent to shortest queue then scanned
def
scan(self, passenger):
scan_time = random.uniform(0.5, 1)
yield
self.env.timeout(scan_time)
#Passengers arrive, to the first available queue for the ID check then sent to the first available scanner.
def
Passenger(env, number, s):
#global average wait time
global
total_time global
total_passengers #Note the start time
Arrivaltime = env.now
with
s.queue.request() as
request:
#passenger in line request queue to help
yield
request
#assign queue to a passenger
yield
env.process(s.IDcheck(number))
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with
s.scanner.request() as
request:
#passenger in line waiting for passport/ID scan
yield
request
#process scanning a passenger
yield
env.process(s.scan(number))
pass_time = env.now - Arrivaltime
total_time = total_time + pass_time
total_passengers = total_passengers+1
def
setup(env, num, security):
arrival_int = random.expovariate(5)
yield
env.timeout(arrival_int)
env.process(Passenger(env, num, security)) # Setup and start the simulation
print('Airport Security Check Stimulation')
## Airport Security Check Stimulation
random.seed(1)
env = sy.Environment()
ap = Airport(env, num_queues, num_scanners)
# Start processes and run
for
i in
range(0,num_passengers):
env.process(setup(env, i, ap))
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## <Process(setup) object at 0x10b412e00>
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## <Process(setup) object at 0x10b42ef80>
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## <Process(setup) object at 0x10b42f280>
## <Process(setup) object at 0x10b42f340>
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## <Process(setup) object at 0x10b42f4c0>
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## <Process(setup) object at 0x10b42f880>
## <Process(setup) object at 0x10b42f940>
## <Process(setup) object at 0x10b42fa00>
## <Process(setup) object at 0x10b42fac0>
## <Process(setup) object at 0x10b42fb80>
10/25/23, 8:29 PM
Week9
file:///Users/veronica/Week9.html
12/15
## <Process(setup) object at 0x10b42fc40>
## <Process(setup) object at 0x10b42fd00>
## <Process(setup) object at 0x10b42fdc0>
## <Process(setup) object at 0x10b42fe80>
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## <Process(setup) object at 0x10b444040>
## <Process(setup) object at 0x10b444100>
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## <Process(setup) object at 0x10b444280>
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## <Process(setup) object at 0x10b445300>
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## <Process(setup) object at 0x10b445d80>
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## <Process(setup) object at 0x10b445f00>
## <Process(setup) object at 0x10b445fc0>
## <Process(setup) object at 0x10b446080>
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## <Process(setup) object at 0x10b446200>
## <Process(setup) object at 0x10b4462c0>
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10/25/23, 8:29 PM
Week9
file:///Users/veronica/Week9.html
13/15
## <Process(setup) object at 0x10b446380>
## <Process(setup) object at 0x10b446440>
## <Process(setup) object at 0x10b446500>
## <Process(setup) object at 0x10b4465c0>
## <Process(setup) object at 0x10b446680>
## <Process(setup) object at 0x10b446740>
## <Process(setup) object at 0x10b446800>
## <Process(setup) object at 0x10b4468c0>
## <Process(setup) object at 0x10b446980>
## <Process(setup) object at 0x10b446a40>
## <Process(setup) object at 0x10b446b00>
## <Process(setup) object at 0x10b446bc0>
## <Process(setup) object at 0x10b446c80>
## <Process(setup) object at 0x10b446d40>
## <Process(setup) object at 0x10b446e00>
## <Process(setup) object at 0x10b446ec0>
## <Process(setup) object at 0x10b446f80>
## <Process(setup) object at 0x10b447040>
## <Process(setup) object at 0x10b447100>
## <Process(setup) object at 0x10b4471c0>
## <Process(setup) object at 0x10b447280>
## <Process(setup) object at 0x10b447340>
## <Process(setup) object at 0x10b447400>
## <Process(setup) object at 0x10b4474c0>
## <Process(setup) object at 0x10b447580>
## <Process(setup) object at 0x10b447640>
## <Process(setup) object at 0x10b447700>
## <Process(setup) object at 0x10b4477c0>
## <Process(setup) object at 0x10b447880>
## <Process(setup) object at 0x10b447940>
## <Process(setup) object at 0x10b447a00>
## <Process(setup) object at 0x10b447ac0>
## <Process(setup) object at 0x10b447b80>
## <Process(setup) object at 0x10b447c40>
## <Process(setup) object at 0x10b447d00>
## <Process(setup) object at 0x10b447dc0>
## <Process(setup) object at 0x10b447e80>
## <Process(setup) object at 0x10b447f40>
## <Process(setup) object at 0x10b828040>
## <Process(setup) object at 0x10b828100>
## <Process(setup) object at 0x10b8281c0>
## <Process(setup) object at 0x10b828280>
## <Process(setup) object at 0x10b828340>
## <Process(setup) object at 0x10b828400>
## <Process(setup) object at 0x10b8284c0>
## <Process(setup) object at 0x10b828580>
## <Process(setup) object at 0x10b828640>
## <Process(setup) object at 0x10b828700>
## <Process(setup) object at 0x10b8287c0>
## <Process(setup) object at 0x10b828880>
## <Process(setup) object at 0x10b828940>
## <Process(setup) object at 0x10b828a00>
10/25/23, 8:29 PM
Week9
file:///Users/veronica/Week9.html
14/15
## <Process(setup) object at 0x10b828ac0>
## <Process(setup) object at 0x10b828b80>
## <Process(setup) object at 0x10b828c40>
## <Process(setup) object at 0x10b828d00>
## <Process(setup) object at 0x10b828dc0>
## <Process(setup) object at 0x10b828e80>
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## <Process(setup) object at 0x10b82ae00>
## <Process(setup) object at 0x10b82aec0>
## <Process(setup) object at 0x10b82af80>
## <Process(setup) object at 0x10b82b040>
## <Process(setup) object at 0x10b82b100>
10/25/23, 8:29 PM
Week9
file:///Users/veronica/Week9.html
15/15
## <Process(setup) object at 0x10b82b1c0>
## <Process(setup) object at 0x10b82b280>
## <Process(setup) object at 0x10b82b340>
## <Process(setup) object at 0x10b82b400>
## <Process(setup) object at 0x10b82b4c0>
## <Process(setup) object at 0x10b82b580>
## <Process(setup) object at 0x10b82b640>
## <Process(setup) object at 0x10b82b700>
## <Process(setup) object at 0x10b82b7c0>
## <Process(setup) object at 0x10b82b880>
## <Process(setup) object at 0x10b82b940>
## <Process(setup) object at 0x10b82ba00>
## <Process(setup) object at 0x10b82bac0>
## <Process(setup) object at 0x10b82bb80>
## <Process(setup) object at 0x10b82bc40>
## <Process(setup) object at 0x10b82bd00>
## <Process(setup) object at 0x10b82bdc0>
## <Process(setup) object at 0x10b82be80>
## <Process(setup) object at 0x10b82bf40>
## <Process(setup) object at 0x10b83c040>
## <Process(setup) object at 0x10b83c100>
## <Process(setup) object at 0x10b83c1c0>
## <Process(setup) object at 0x10b83c280>
## <Process(setup) object at 0x10b83c340>
## <Process(setup) object at 0x10b83c400>
## <Process(setup) object at 0x10b83c4c0>
## <Process(setup) object at 0x10b83c580>
## <Process(setup) object at 0x10b83c640>
## <Process(setup) object at 0x10b83c700>
## <Process(setup) object at 0x10b83c7c0>
## <Process(setup) object at 0x10b83c880>
## <Process(setup) object at 0x10b83c940>
env.run()
avg_time = total_time / total_passengers
print(f'Average wait time is {avg_time}')
## Average wait time is 15.298647678446711
As we can see from the average wait time in ATL airport is 15.3 minutes per check in process. In this case, to
faster the scanning process and lower the passengers wait time. We suggest the airport should increase the
available scanner as well as increase the queues when there are some traffic.
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