Homework Week 9 - Solution
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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 felo1998
Homework Week 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.
Design of experiments can be used in the commercial aviation industry for different services that have general customer satisfaction as an indicator. For in-flight services, it can be of great help to determine, for example, which food menu may have the best combination between cost and satisfaction, varying portions, presentation, and options.
Another use may be related to the entertainment system and advertisements. With each person having their own entertainment system, they could use different entertainment offers on the same flight between movies, series, music and see how much engagement they generate depending on the options. To be translated into revenue, that engagement could be combined with what type of ads and at what time of the flight are displayed on passengers' screens and collect information on how effective those ads are.
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.
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).
Keeping it in the aviation/aerospace industry context, I think the following can be good examples for each distribution:
a. Binomial Number of successful takeoffs out of a series of flights.
b. Geometric Number of unsuccessful attempts to land an aircraft before a successful landing.
c. Poisson Number of bird strikes (random event).
d. Exponential Time between equipment failures during regular maintenance operations (rate is constant over time)
e. Weibull
Lifespan of specific aircraft component (parts of engine that wear out over 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.]
Note: -
I had some difficulties with exporting the results to excel so I used the SIMAN summary report option. However, for this one I didn’t get results for the average of all replications. Instead, I had results for every replication separately in the wait time and total time parameters which are the ones that concern us. I will read about how to export properly the results for future study cases, but for this homework I will briefly analyze one replication for every run (which I understand is not ideal at all).
I tried initially proposing models with different configurations:
1.
3 ID/Boarding Pass Checkers and 3 Scanners
2.
4 ID/Boarding Pass Checkers and 3 Scanners
3.
3 ID/ Boarding Pass Checkers and 4 Scanners
However, they all generated a bottle neck behavior and exceeded the 150 simultaneous entities limit set by the Student version of Arena when setting the replication length for more than 2 hours. After these tries, I tested the following model with 4 ID/Boarding Pass Checkers and 4 Scanners.
This model generated the following output:
We can see how the Maximum Entity 1.TotalTime does not exceed our 15min goal (Again, I tried simulating with less resources to be able to get an average closer to 15 mins but the 150 entity limit didn’t allow me to run the model for more than theoretical 2 hours). We can see also see how the wait time is double the time than our value added which is actually a not bad indicator when we put into context. The wait times are very similar when comparing Boarding pass checkpoint to
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Scanner checkpoint, this indicates that we have a good even flow and that it is unlikely for us to fall in a bottle neck behavior. If we wanted we could increase the value added/wait time ratio by increasing resources in both checkpoint, however we have averages that are pretty well distributed for the test case application.