Practice Problems: Chapter 4, Forecasting
Problem 1:
Auto sales at Carmen’s Chevrolet are shown below. Develop a 3-week moving average.
Week
Auto
Sales
1
8
2
10
3
9
4
11
5
10
6
13
7
-
Problem 2:
Carmen’s decides to forecast auto sales by weighting the three weeks as follows:
Weights
Applied
Period
3
Last week
2
Twoweeks
ago
1
Three
weeks ago
6
Total
1
Problem 3:
A firm uses simple exponential smoothing with   0.1 to forecast demand. The forecast
for the week of January 1 was 500 units whereas the actual demand turned out to be 450
units. Calculate the demand forecast for the week of January 8.
Problem 4:
Exponential smoothing is used to forecast automobile battery sales. Two value of  are
examined,   0.8 and   0.5. Evaluate the accuracy of each smoothing constant. Which
is preferable? (Assume the forecast for January was 22 batteries.) Actual sales are given
below:
Month
Actual Forecast
Battery
Sales
January
20
22
February 21
March
15
April
14
May
13
June
16
Problem: 5
Over the past year Meredith and Smunt Manufacturing had annual sales of 10,000
portable water pumps. The average quarterly sales for the past 5 years have averaged:
spring 4,000, summer 3,000, fall 2,000 and winter 1,000. Compute the quarterly index.
Problem: 6
Using the data in Problem 5, Meredith and Smunt Manufacturing expects sales of pumps
to grow by 10% next year. Compute next year’s sales and the sales for each quarter.
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ANSWERS:
Problem 1:
Moving average =
 demand in previous n periods
n
Week
Auto
Sales
Three-Week
Average
Moving
1
8
2
10
3
9
4
11
(8 + 9 + 10) / 3 = 9
5
10
(10 + 9 + 11) / 3 = 10
6
13
(9 + 11 + 10) / 3 = 10
7
-
(11 + 10 + 13) / 3 = 11
1/3
3
Problem 2:
Weighted moving average =
 (weight for period n)(demand in period n)
 weights
Week
Auto
Sales
Three-Week Moving Average
1
8
2
10
3
9
4
11
[(3*9) + (2*10) + (1*8)] / 6 = 9 1/6
5
10
[(3*11) + (2*9) + (1*10)] / 6 = 10 1/6
6
13
[(3*10) + (2*11) + (1*9)] / 6 = 10 1/6
7
-
[(3*13) + (2*10) + (1*11)] / 6 = 11 2/3
Problem 3:
Ft  Ft 1   (A t 1  Ft 1 )  500  0.1(450  500)  495 units
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Problem 4:
Month
Actual
Rounded
Battery Sales Forecast
with a =0.8
Absolute
Deviation
with a =0.8
Rounded
Forecast
with a =0.5
Absolute
Deviation
with a =0.5
January
20
22
2
22
2
February
21
20
1
21
0
March
15
21
6
21
6
April
14
16
2
18
4
May
13
14
1
16
3
June
16
13
3
14.5
1.5
SE
S = 15
S = 16
2.56
2.95
3.5
3.9
On the basis of this analysis, a smoothing constant of a = 0.8 is preferred to that of a
= 0.5 because it has a smaller MAD.
Problem 5:
Sales of 10,000 units annually divided equally over the 4 seasons is 10,000 / 4  2,500
and the seasonal index for each quarter is: spring 4,000 / 2,500  1.6; summer
3,000 / 2,500  1.2; fall 2,000 / 2,500 .8; winter 1,000 / 2,500 .4.
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Problem 6:
Next years sales should be 11,000 pumps (10,000 *110
.  11,000). Sales for each quarter
should be 1/4 of the annual sales * the quarterly index.
Spring = (11,000 / 4)*1.6 = 4,400;
Summer = (11,000 / 4)*1.2 = 3,300;
Fall = (11,000 / 4)*.8 = 2,200;
Winter = (11,000 / 4)*.4.=1,100.
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