Homework Week 4 - 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
3
Uploaded by felo1998
Homework Week 4.
Question 7.1
Describe a situation or problem from your job, everyday life, current events, etc., for which exponential smoothing would
be appropriate. What data would you need? Would you expect the value of α (the first smoothing parameter) to be closer
to 0 or 1, and why?
In the cargo industry, goods and products move throughout the year, each with different demand behaviors. The analysis of market
behavior can be useful when planning the company's capacity, distribution of efforts and reservation of warehouse space during
certain periods.
In the airline where I work, flowers are imported from Colombia and Ecuador to the United States with very marked seasons of high
demand in the months of February (Valentine's) and May (Mother's Day). For this seasonality behavior, exponential smoothing can be
a very successful model. The alpha value would be expected to be close to 0 to reduce sensitivity to short-term changes and to "rely"
more on historical data from previous seasons.
An exponential smoothing model could also be implemented for each family of products, each with an alpha depending on the case, in
order to have an estimated prediction of demand and make decisions on how to divide and allocate the physical space in the
warehouse and in the coolers (case of flowers and perishable products).
https://secondmeasure.com/datapoints/flower-companies-pandemic/
Question 7.2
Using the 20 years of daily high temperature data for Atlanta (July through October) from Question 6.2 (file temps.txt), build and use
an exponential smoothing model to help make a judgment of whether the unofficial end of summer has gotten later over the 20 years.
(Part of the point of this assignment is for you to think about how you might use exponential smoothing to answer this question. Feel
free to combine it with other models if you’d like to. There’s certainly more than one reasonable approach.)
Note: in R, you can use either HoltWinters (simpler to use) or the smooth package’s es function (harder to use, but more general).
If
you use es, the Holt-Winters model uses model=”AAM” in the function call (the first and second constants are used “A”dditively, and
the third (seasonality) is used “M”ultiplicatively; the documentation doesn’t make that clear).
To run the HoltWinters model in R, I imported the data and converted it into a time-series for an input of 2460 divided into years of
123 frequencies (123 days from July 1 to October 31).
A multiplicative approach was chosen because of the evident seasonality seen in the plot and the nature of the data. Alpha, beta and
gamma values were set null for the model to choose which value worked best. The model produced these following values:
We can see a balanced alpha, giving close to equal weigh to past and present data, a 0-beta representing no trend as seen in the
graphic, and a gamma of 0,5 that gives a bit of priority to that seasonal factor present in our data.
After running the model, we get a smoother graph from 1997 to 2016 (first year works as base) and export the data to excel as seen in
the graph and code below:
In excel, I used CUSUM to answer the question if end of summer has gotten later over the 20 years. I used C and T values similar to the
ones in last week model to avoid “punishing” the output data for being previously smoothed.
The blue row indicates the number of days that passed before exceeding the 18 Threshold, and as shown in the graph below, The data
does have a downward trend line, but it is minimal and possibly impacted by the year 2013, with a value that could probably be
classified as an outlier with further analysis. Because of this, it is my opinion that the end of summer has not moved on average over
the last 20 years.
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