Problem1(20 points)
Maximum pages: 3
REI is a national retail store that specializes in outdoor recreational clothing.Demand for its items is very seasonal, peaking in spring and then in summer. It accumulated the following data ($million sales) during the past 5 years on one product line – hunting clothing.
|
Sales Volume (in $Million)
|
Year
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2015
|
2016
|
2017
|
2018
|
2019
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Jan-Mar
|
18.6
|
18.1
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22.4
|
23.2
|
24.5
|
Apr-Jun
|
23.5
|
24.7
|
28.8
|
27.6
|
31
|
Jul-Sept
|
41.9
|
46.3
|
45.5
|
47.1
|
52.8
|
Oct-Dec
|
20.4
|
19.5
|
21
|
24.4
|
23.7
|
- Estimate the quarterly seasonal indices. (3 pts)
- Using the quarterly seasonal indexes you developed in number 1, deseasonalize the quarterly sales for the years 2015 to 2019. (3 pts)
- Create a time series graph showing : (5 pts)
- the actual sales, by quarter, from 2015 to 2019
- the deseasonalized quarterly volume of sales for the same time period, and
- the trend line of the deseasonalized sales volume.Show in your graph the trend line as well as the linear equation of that trend line.
Label the graph completely and accurately. Point will be deducted for graph not properly labeled.
- Using the trend equation you developed in number 3, give yourseasonally adjustedforecast for the quarterly sales in 2020. (4 pts)
- Discuss what the consequences will be for REI if they simply used the trend forecasting model developed in #3c, without adjusting for seasonality (e.g. if they fail to adjust the trend forecast for seasonality) of the sales.In your discussion, address any important decisions, related to their operations, that they might make wherein the forecast information will be critical. (5 points)
Problem2(20 points)
Maximum pages: 2
Using the REI time series data in problem 1,
1.Develop a seasonally adjusted quarterly forecast for the years 2015 to 2019 using the following techniques. And for each technique, compute the MAD and MSE.Present your forecasts in tabular form – periods in rows, forecasting techniques in columns, and MAD and MSE at the bottom of each column.The table should occupy one page only. (8 pts)
a.Naïve
b.4-quarter moving average
c.Exponential smoothing using a smoothing constant of 0.20
d.Seasonally adjusted linear trend forecast developed in Problem 1.4 (previous problem)
2.Prepare a line graph of the original data and plot within the graph the quarterly forecasts you developed in #1 above. Label the components of the graph completely and clearly. (8 points)
3.Based on your answers to #1 and #2 above, which of the forecasting techniques would you recommend to use? Explain – do not express unsupported opinions here.(4 points)
Problem 3 (20)
Maximum pages: 2
In a manufacturing process, the batch size was thought to affect the number of defective parts that are produced by the process. To test this theory, management devised an experiment where a
batch is run and then checked.All units in the batch that do not meet required certain characteristics discarded. Thirty (30) batches were run, and the number of defectives in each batch was counted.The results are shown below.
Click here
to download the data in Excel.
a.Develop a model that relates the batch size to the number of defective parts produced. Show your output below for your selected model. Explain why and how you chose that model. (5 points)
b.Using the model you developed in part (a), estimate the number of defective parts found for a batch size of 330. Show how you arrived at your estimate. (5 points)
c.Based on the forecasting model you developed in part (a), explain the relationship between batch size and number of defectives produced. Your explanation should include discussion of the nature of the relationship (e.g. linear or nonlinear, direct or inverse, the strength of association between the variables, and how well (or poorly) the batch size impacts the variation in number of defective parts produced by the manufacturing process. Support your explanation with appropriate numeric measures. Opinions, suppositions, and unfounded explanations are to be avoided. (10 points)
PERSONAL REFLECTION (TAKEAWAYS) – 20 points
(no more than one page)