Chapter 4, Heizer/Render, 7th edition

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Practice Problems
Problem 1:
Auto sales at Carmen’s Chevrolet are shown below. Develop a 3-week
moving average and develop a forecast for Week 7.
Week
1
2
3
4
5
6
7
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Auto Sales
8
10
9
11
10
13
—
4-1
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Problem 1:
Practice Problems
demand in previous n periods
Moving average =
n
Auto sales at Carmen’s Chevrolet are shown below. Develop a 3-week
moving average and develop a forecast for Week 7.
Week
1
2
3
4
5
6
7
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Auto Sales
8
10
9
11
10
13
—
4-2
3–Week Moving Average
(8 + 10 + 9)/3 = 9
(10 + 9 + 11)/3 = 10
(9 + 11 + 10)/3 = 10
(11 + 10 + 13)/3 = 111/3
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Practice Problems
Problem 2:
Carmen’s decides to forecast auto sales by weighting the three weeks as
follows:
Weights Applied
3
2
1
6
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Period
Last week
Two weeks ago
Three weeks ago
Total
4-3
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Practice Problems
Week
Auto Sales
3–Week Moving Average
1
8
10
Problem 2: 2
3
9
4 to forecast auto11
(3*9 +the
2*10
+ 1*8)/6
= 9as1/6
Carmen’s decides
sales by weighting
three
weeks
5
10
(3*11 + 2*9 + 1*10)/6 = 101/6
follows:
6
13
(3*10 + 2*11 + 1*9)/6 = 101/6
7
—
(3*13 + 2*10 + 1*11)/6 = 112/3
Weights Applied
Period
3
Last week
2
Two weeks ago
1
Three weeks ago
6
Total
(weight for period n)(demand in period n)
Moving average =
weights
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© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Practice Problems
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.
Ft = Ft-1 + (At-1 – Ft-1) = 500 + 0.1(450 – 500) = 495 units
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© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Practice Problems
Problem 4:
Exponential smoothing is used to forecast automobile battery sales. Two
values 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 Battery Sales
January
20
February
21
March
15
April
14
May
13
June
18
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Practice Problems
|deviations|
MAD =
n
Problem 4:
Exponential smoothing is used to forecast automobile battery sales. Two
values 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:
Absolute
Absolute
Month Actual Battery Sales Forecast  =Deviation
0.8 Forecast  =Deviation
0.5
2
2
January
20
22
22
1
0
February
21
20
21
6
6
March
15
21
21
2
4
April
14
16
18
1
3
May
13
14
16
3
1.5
June
18
13
14.5
MAD = 2.56
MAD = 2.67
 = 15
 = 16
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
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4-7
Practice Problems
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
1996
1997
1998
1999
2000
2001
2002
Sales (Units)
100
110
122
130
139
152
164
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© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Practice Problems
x
28

x= n =
=4
y = a + bx = 89.16 + 10.46x
7
Problem 5:
y 917
y= n =
= 131
7
Use the sales data given
below to determine: (a) the least squares trend line,
3961
– (7)(4)(131)
xy
–
nxy
293
and (b) bthe
predicted
value
for
2003
sales.
=
=
=
= 10.46
140 – (7)(42)
 x2 – nx2
28
Year
Sales (Units) Time Period
X2
XY
a = y – bx = 131 – (10.46*4) = 89.16
1996
100
1
1
100
1997
110
2
4
220
1998
122
3
9
366
1999
130
4
16
520
Sales in 2003 =589.16 + 10.46*8
2000
139
25 = 172.84
695
2001
152
6
36
912
2002
164
7
49
1148

917
28
140
3961
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© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Practice Problems
Problem 6:
Given the forecast demand and actual demand for 10-foot fishing boats,
compute the tracking signal and MAD.
Year
1
2
3
4
5
6
Forecast
Demand
78
75
83
84
88
85
Actual
Demand
71
80
101
84
60
73
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© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Problem 6:
Practice Problems
|Forecast errors|
MAD =
n
=
70
= 11.7
6
Given the forecast demand and actual demand for 10-foot fishing boats,
compute the tracking signal and MAD.
Year
1
2
3
4
5
6
Forecast
Demand
78
75
83
84
88
85
Actual
Demand
71
80
101
84
60
73
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Error
–7
5
18
0
–28
–12
4-11
RSFE
–7
–2
16
16
–12
–24
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Problem 6:
Practice Problems
RSFE
Tracking Signal =
MAD
=
–24
= 2.1 MADs
11.7
Given the forecast demand and actual demand for 10-foot fishing boats,
compute the tracking signal and MAD.
Year
1
2
3
4
5
6
Forecast
Demand
78
75
83
84
88
85
Actual
Demand
71
80
101
84
60
73
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Cummulative
|Error|
Error
7
7
5
12
18
30
0
30
28
58
12
70
4-12
MAD
7.0
6.0
10.0
7.5
11.6
11.7
Tracking
Signal
–1.0
–0.3
+1.6
+2.1
–1.0
–2.1
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Practice Problems
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.
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© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Practice Problems
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.
Equally dividing the annual sales of
10,000 units over the four seasons
Spring
Summer
Fall
Winter
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10,000 / 4 = 2,500
4,000 / 2,500 = 1.6
3,000 / 2,500 = 1.2
2,000 / 2,500 = 0.8
1,000 / 2,500 = 0.4
4-14
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Practice Problems
Problem 8:
Using the data in Problem 7, 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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© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458
Practice Problems
Problem 8:
Using the data in Problem 7, 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.
Next years sales should be 11,000 pumps (10,000*1.10 = 11,000)
Spring
Summer
Fall
Winter
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(11,000 / 4)*1.6 = 4,400
(11,000 / 4)*1.2 = 3,300
(11,000 / 4)*0.8 = 2,200
(11,000 / 4)*0.4 = 1,100
4-16
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458

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