Forecasting & Smoothing Methods
Solved Problem #1: see text book
Solved Problem #2: see textbook (manual example using seasonal relatives)
Solved Problem #3: see textbook
Solved Problem #4: see textbook (you do not have to do this problem manually, use the template and notice how the template answers differ slightly from the seasonal relatives provided in the manual example)
To avoid manually entering the data into the templates it can be copied and pasted from Data Sets on the Lesson Page. Use “copy, paste special, values” to transfer the data to the template.
#1: A commercial bakery has recorded sales (in dozens) for three products, as shown below.
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Day |
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Blueberry |
Cinnamon |
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Cupcakes |
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|
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Muffins |
buns |
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||
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|
1 |
|
30 |
18 |
|
45 |
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|
|
|
2 |
|
34 |
17 |
|
26 |
|
|
|
|
|
3 |
|
32 |
19 |
|
27 |
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|
|
|
|
4 |
|
34 |
19 |
|
23 |
|
|
|
|
|
5 |
|
35 |
22 |
|
22 |
|
|
|
|
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6 |
|
30 |
23 |
|
48 |
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|
|
|
|
7 |
|
34 |
23 |
|
29 |
|
|
|
|
|
8 |
|
36 |
25 |
|
20 |
|
|
|
|
|
9 |
|
29 |
24 |
|
14 |
|
|
|
|
|
10 |
|
31 |
26 |
|
18 |
|
|
|
|
|
11 |
|
35 |
27 |
|
47 |
|
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|
|
12 |
|
31 |
28 |
|
26 |
|
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|
|
|
13 |
|
37 |
29 |
|
27 |
|
|
|
|
|
14 |
|
34 |
31 |
|
24 |
|
|
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|
|
15 |
|
33 |
33 |
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22 |
|
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a. Determine the Naïve forecast for day 16. |
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b. What does the use of sales data rather than demand data imply?
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Month |
Sales |
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Feb |
19 |
|
Mar |
18 |
|
Apr |
15 |
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May |
20 |
|
Jun |
18 |
|
Jul |
22 |
|
Aug |
20 |
1. Naïve
2. Five-month moving average
3. Weighted moving average using .60 for August, .30 for July, and .10 for June
4. Exponential smoothing with a smoothing constant of .20
5. Linear trend equation.
Ft =80+15t where
F t= annual sales (000 bottles)
t = 0corresponds to1990
#4: Freight car loadings over a 12-year period at a busy port are as follows: The units are in thousands of tons.
|
Year |
Loadings |
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1 |
220 |
|
2 |
245 |
|
3 |
280 |
|
4 |
275 |
|
5 |
300 |
|
6 |
310 |
|
7 |
350 |
|
8 |
360 |
|
9 |
400 |
|
10 |
380 |
|
11 |
420 |
|
12 |
450 |
|
13 |
460 |
|
14 |
475 |
|
15 |
500 |
|
16 |
510 |
|
17 |
525 |
|
18 |
541 |
|
Use the trend equation to predict the freight loadings for years 20 and 21. |
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d. |
The manager intends to install new equipment when the loadings exceeds 800 (thousand tons) per |
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year. Assuming the current trend continues the loading volume will reach that level in |
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approximately what year? This is a manual problem! |
#5: A manager of a store that sells and installs spas wants to prepare a forecast for January, February and March of next year. Her forecasts are a combination of trend and seasonality.
The linear trend equation is
Ft =70+5t where
t =0 corresponds to June of last year
The seasonal relatives are 1.10 for January, 1.02 for February, and .95 for March.
|
Day |
Served |
|
1 |
80 |
|
2 |
75 |
|
3 |
78 |
|
4 |
95 |
|
5 |
130 |
|
6 |
136 |
|
7 |
40 |
|
8 |
82 |
|
9 |
77 |
|
10 |
80 |
|
11 |
94 |
|
12 |
125 |
|
13 |
135 |
|
14 |
42 |
|
15 |
84 |
|
16 |
77 |
|
17 |
83 |
|
18 |
96 |
|
19 |
135 |
|
20 |
140 |
|
21 |
37 |
|
22 |
87 |
|
23 |
82 |
|
24 |
98 |
|
25 |
103 |
|
26 |
144 |
|
27 |
144 |
|
28 |
48 |
a. Construct a graph that will enable you to visualize the daily variation in meals served.
b. What are the daily adjusted seasonal relatives?
c. Plot the adjusted seasonal relatives on a graph for each day of the week?
#7: A farming cooperative manager wants to estimate quarterly relatives for grain shipments, based on the 5 years of data shown below (quantities are in metric tons). You will have to enter this data into the template manually.
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QUARTER |
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|
Year |
1 |
2 |
3 |
4 |
|
1 |
200 |
250 |
210 |
340 |
|
2 |
210 |
252 |
212 |
360 |
|
3 |
215 |
260 |
220 |
358 |
|
4 |
225 |
272 |
233 |
372 |
|
5 |
232 |
284 |
240 |
381 |
a. Calculate the quarterly adjusted seasonal relatives.
b. Use the adjusted seasonal relative to determine what percentage shipments in quarter 4 are greater than shipments quarter 3.
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