1. 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
1

2. 6
Total
Problem 3:
A firm uses simple exponential smoothing with α = 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 α are
examined, α = 0.8 and α = 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
2

3. Problem 5:
Use the sales data given below to determine: (a) the least squares trend line, and (b) the
predicted value for 2003 sales.
Year Sales
(Units)
1996 100
1997 110
1998 122
1999 130
2000 139
2001 152
2002 164
To minimize computations, transform the value of x (time) to simpler numbers. In this
case, designate year 1996 as year 1, 1997 as year 2, etc.
3

4. Problem 6:
Given the forecast demand and actual demand for 10-foot fishing boats, compute the
tracking signal and MAD.
Year Forecast Actual
Demand Demand
1
78
71
2
75
80
3
83
101
4
84
84
5
88
60
6
85
73
Problem: 7
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: 8
Using the data in Problem, 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.
4

5. ANSWERS:
Problem 1:
Moving average =
∑ demand in previous n periods
Three-Week
Average
n
Week
Auto
Sales
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
5

6. 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 + α ( A t −1 − Ft −1 ) = 500 + 0.1( 450 − 500) = 495 units
6

7. 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
S = 15
2.56
2.95
3.5
SE
S = 16
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.
7

8. Problem 5:
Year
Time Sales
X2
Period (Units)
(X)
(Y)
XY
1996
1
100
1
100
1997
2
110
4
220
1998
3
122
9
366
1999
4
130
16
520
2000
5
139
25
695
2001
6
152
36
912
2002
7
164
49
1148
S X = S
Y S
S XY
28
=917
X2=140 =
3961
x=
∑ x = 28 = 4
y=
∑ y = 917 = 131
b=
n
7
n
7
∑ xy − nxy = 3961 − (7)(4)(131) = 293 = 10.46
140 − (7)( 4 )
28
∑ x − nx
2
2
2
a = y − bx = 131 − (10.46 × 4) = 89.16
Therefore, the least squares trend equation is:

y = a + bx = 89.16 + 10.46 x
To project demand in 2003, we denote the year 2003 as x = 8, and:
Sales in 2003 = 89.16 + 10.46 * 8 = 172.84
8

9. Problem 6:
Year Forecast Actual
Error RSFE
Demand Demand
1
78
71
-7
-7
2
75
80
5
-2
3
83
101
18
16
4
84
84
0
16
5
88
60
-28
-12
6
85
73
-12
-24
MAD =
∑ Forecast errors
n
=
70
= 11.7
6
Year Forecast Actual
|Forecast Cumulative MAD Tracking
Demand Demand Error|
Error
Signal
1
78
71
7
7
7.0
-1.0
2
75
80
5
12
6.0
-0.3
3
83
101
18
30
10.0
+1.6
4
84
84
0
30
7.5
+2.1
5
88
60
28
58
11.6
-1.0
6
85
73
12
70
11.7
-2.1
Tracking Signal =
RFSE −24
=
= 2.1 MADs
MAD 11.7
9

10. Problem 7:
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.
Problem 8:
.
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.
10