Lesson 05 Forecasting & Smoothing Methods Solutions
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
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
a.
Cinnamon
buns
18
17
19
19
22
23
23
25
24
26
27
28
29
31
33
Cupcakes
45
26
27
23
22
48
29
20
14
18
47
26
27
24
22
Cinnamon
buns
33
Cupcakes
22
Determine the Naïve forecast for day 16.
Day
16
b.
Blueberry
Muffins
30
34
32
34
35
30
34
36
29
31
35
31
37
34
33
Blueberry
Muffins
33
What does the use of sales data rather than demand data imply?
Sales data does not take into account the demand which may have been greater than the
actual sales. If the demand was actually greater than sales and the bakery could have met
that demand, using sales would cause them to under forecast their full business potential.
1
#2: National Scan, Inc., sells radio frequency inventory tags. Monthly sales ($000) for a seven-month
period were as follows:
Month
Feb
Mar
Apr
May
Jun
Jul
Aug
a.
Sales
19
18
15
20
18
22
20
Plot the monthly data.
Historical Data
25
20
15
10
5
0
0
1
2
3
4
5
6
7
8
Period
Sales
b.
Forecast September sales volume in thousands of dollars using the following methods: Show your
answers in the space provided.
1.
2.
3.
4.
5.
Naïve
Five-month moving average
Weighted moving average using .60 for August, .30 for July, and .10 for June
Exponential smoothing with a smoothing constant of .20
Linear trend equation.
Month
Sep
Naive
20
MA
19
WMA
20.4
ES
19.26
LT
20.86
2
#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.
Ft = 80 + 15t where
F t = annual sales (000 bottles )
t = 0 corresponds to 1990
a.
Indicate how much the sales are increasing or decreasing?
Sales are increasing by 15,000 bottles per year
b.
Predict sales for the year 2006 using the equation? This is a manual problem!
t = 16 therefore the forecast for the year 2006 = 80 + 16*15 = 320 thousand bottles
#4: Freight car loadings over a 12-year period at a busy port are as follows: The units are in thousands of
tons.
Year
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
a.
Loadings
220
245
280
275
300
310
350
360
400
380
420
450
460
475
500
510
525
541
Determine the linear trend equation for the freight car loadings.
Forecast = 208.48 + 19 * year
b.
What is the slope? Interpret it.
Slope = 19 thousand pounds
Interpretation: the freight loadings are increasing 19 thousand pounds per year
3
c.
Use the trend equation to predict the freight loadings for years 20 and 21.
Year
20
21
d.
Loadings
588.40
607.40
The manager intends to install new equipment when the loadings exceeds 800 (thousand tons) per
year. Assuming the current trend continues the loading volume will reach that level in
approximately what year? This is a manual problem!
Solving the equation for t yields t = 31.13 years
#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.
a.
What demand should she predict for January, February and March of next year? This is a manual
problem! If you need some hints on this problem, refer to solved problem #2 in the textbook.
January
181.5
February
173.4
March
166.25
4
#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
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
Served
80
75
78
95
130
136
40
82
77
80
94
125
135
42
84
77
83
96
135
140
37
87
82
98
103
144
144
48
5
a. Construct a graph that will enable you to visualize the daily variation in meals served.
Historical Data
160
140
120
100
80
60
40
20
0
0
5
10
15
20
25
30
Period
Served
What are the daily adjusted seasonal relatives?
Day
1
2
3
4
5
6
7
Plot the adjusted seasonal relatives on a graph for each day of the week?
0.
42
56
1.
03
12
0.
91
60
0.
83
34
1.6000
1.4000
1.2000
1.0000
0.8000
0.6000
0.4000
0.2000
0.0000
1.
41
16
Adjusted Seasonal Relative (ASR)
0.
89
97
c.
Adjusted
Seasonal
Relative
0.8997
0.8334
0.9160
1.0312
1.4116
1.4825
0.4256
1.
48
25
b.
Per io d 1
Per io d
2
Per io d
3
Per io d
4
Per io d
5
Per io d
6
Per io d
7
6
d.
Determine the forecast for meals to be served for the next 7 days.
Day
1
2
3
4
5
6
7
e.
Forecast
91.36
85.05
93.95
106.30
146.23
154.33
44.53
Plot historical demand with forecast on the same graph.
Historical Data & Seasonally Adjusted Linear Trend
180
160
140
120
100
80
60
40
20
0
0
10
20
30
40
Served
50
60
70
Forecast
#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
5
1
200
210
215
225
232
2
250
252
260
272
284
3
210
212
220
233
240
4
340
360
358
372
381
7
a.
Calculate the quarterly adjusted seasonal relatives.
Quarter
1
2
3
4
b.
Adjusted
Seasonal
Relative
0.8262
0.9919
0.8321
1.3499
Use the adjusted seasonal relative to determine what percentage shipments in quarter 4 are greater
than shipments quarter 3.
Quarter 4 shipments are 62.23% greater than shipments in quarter 3.
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