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.


Day 

Blueberry 
Cinnamon 

Cupcakes 





Muffins 
buns 






1 

30 
18 

45 




2 

34 
17 

26 




3 

32 
19 

27 




4 

34 
19 

23 




5 

35 
22 

22 




6 

30 
23 

48 




7 

34 
23 

29 




8 

36 
25 

20 




9 

29 
24 

14 




10 

31 
26 

18 




11 

35 
27 

47 




12 

31 
28 

26 




13 

37 
29 

27 




14 

34 
31 

24 




15 

33 
33 

22 


a. Determine the Naïve forecast for day 16. 





b. What does the use of sales data rather than demand data imply?
#2: National Scan, Inc., sells radio frequency inventory tags. Monthly sales ($000) for a sevenmonth period were as follows:
Month 
Sales 
Feb 
19 
Mar 
18 
Apr 
15 
May 
20 
Jun 
18 
Jul 
22 
Aug 
20 
1. Naïve
2. Fivemonth 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.
#3: A cosmetics manufacturer’s marketing department has developed a linear trend equation that can be used to predict annual sales of its popular Hand & Foot Cream.
F_{t} =80+15t where
F _{t}= annual sales (000 bottles)
t = 0corresponds to1990
#4: Freight car loadings over a 12year period at a busy port are as follows: The units are in thousands of tons.
Year 
Loadings 
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 
#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
F_{t} =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.
#6: Obtain estimates of daily relatives for the number of customers at a restaurant for the evening meal given the past 4 weeks of historical data. Day 1 is day 1 of week 1, day 8 is day 1 of week 2, etc.
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.


QUARTER 


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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