Download Solutions to Problems in Chapter 1

Chapter 7 Study Guide Solutions
Selected Solutions to Problems in Chapter 7
Problem 1
The number of cans of soft drinks sold in a machine each week is recorded below.
Develop forecasts for periods 1-11 using a three period moving average using
thefollowing
soft drink sales numbers: 122, 85, 92, 98, 110, 108, 115, 102, 95, 98.
Time
Period
1
2
3
4
5
6
7
8
9
10
Time Series
Value
122
85
92
98
110
108
115
102
95
98
Forecast
Forecast
Error
99.67
91.67
100.00
105.33
111.00
108.33
104.00
-1.67
18.33
8.00
9.67
-9.00
-13.33
-6.00
MA3- Forecast Period 4 = (122+85+92)/3 = 99.67
MA3- Forecast Period 5 = (85+92+98)/3 = 91.67
etc.
MA3- Forecast Period 11 = (102+95+98)/3 =
98.33
Problem 2
The number of cans of soft drinks sold in a machine each week is recorded below.
Calculate the mean square error for a three period moving average using the following
soft drink sales numbers: 122, 85, 92, 98, 110, 108, 115, 102, 95, 98.
n
Mean Square Error =
MSE 
The Mean Square Error
 (Y  Ŷ )
t 1
t
n
113.02
SG7-1
t
2
Chapter 7 Study Guide Solutions
Problem 3
Use a four period moving average to forecast attendance at baseball games for period 11.
Historical records show: 2863, 2481, 3239, 3519, 3349, 3637, 3501, 3892, 3732, 3526.
Time
Period
1
2
3
4
5
6
7
8
9
10
Time Series
Value
2,863
2,481
3,239
3,519
3,349
3,637
3,501
3,892
3,732
3,526
Forecast
Forecast
Error
3,025.50
3,147.00
3,436.00
3,501.50
3,594.75
3,690.50
323.50
490.00
65.00
390.50
137.25
-164.50
MA4- Forecast Period 5 = (2,863+2,481+3,239+3,519)/4 = 3,025.50
MA4- Forecast Period 6 = (2,481+3,239+3,519+3,349)/4 = 3,147.00
etc.
MA4- Forecast Period 11 = (3,501+3,892+3,732+3,526)/4 = 3,662.75
Problem 4
Use a four period moving average to calculate mean square error for attendance at
baseball games. Historical records show: 2863, 2481, 3239, 3519, 3349, 3637, 3501,
3892, 3732, 3526.
n
Mean Square Error =
MSE 
The Mean Square Error
 (Y  Ŷ )
t 1
t
n
91,227.55
SG7-2
t
2
Chapter 7 Study Guide Solutions
Problem 5
A hospital records the number of floral deliveries its patients receive each day. For a two
week period, the records show: 25, 30, 32, 38, 42, 37, 39, 34, 31, 36, 33, 29, 31, 28. Use
exponential smoothing with a smoothing constant of 0.4 to forecast the number of
deliveries for periods 2-15.
Time Period Time Series Value-AT
1
25
2
30
3
32
4
38
5
42
6
37
7
39
8
34
9
31
10
36
11
33
12
29
13
31
14
28
Forecast
Forecast Error
25.00
27.00
29.00
32.60
36.36
36.62
37.57
36.14
34.09
34.85
34.11
32.07
31.64
5.00
5.00
9.00
9.40
0.64
2.38
-3.57
-5.14
1.91
-1.85
-5.11
-1.07
-3.64
General exponential smoothing equation:
FT 1  (1 )* FT   * AT
F2  (1 )* F1   * A1 = (1.0 - 0.4)*25 + 0.4*25 = 25
F3  (1 )* F2   * A2 = (1.0 - 0.4)*25 + 0.4*30 = 27
F4 (1 )*F3   * A3 = (1.0 - 0.4)*27 + 0.4*32 = 29
etc.
F15 (1 )*F14   * A14 = (1.0 - 0.4)*31.64 + 0.4*28 = 30.18
SG7-3
Chapter 7 Study Guide Solutions
Problem 6
A hospital records the number of floral deliveries its patients receive each day. For a two
week period, the records show: 25, 30, 32, 38, 42, 37, 39, 34, 31, 36, 33, 29, 31, 28. Use
exponential smoothing with a smoothing constant of 0.4 to calculate the mean square
error.
n
Mean Square Error =
MSE 
 (Y  Ŷ )
t 1
t
2
t
n
The Mean Square Error
24.02
Problem 7
The number of girls who attend a summer basketball camp has been recorded for the
seven years the camp has been offered. Use exponential smoothing with a smoothing
constant of 0.8 to forecast attendance for the eighth year. The number of girls attending
camp are: 95, 110, 163, 147, 172, 175, 183.
Time Period
1
2
3
4
5
6
7
Time Series Value
95
110
163
147
172
175
183
Forecast
Forecast Error
95.00
107.00
151.80
147.96
167.19
173.44
FT 1  (1 )* FT   * AT
F2  (1 )* F1   * A1 = (1.0 - 0.8)*95 + 0.8*95 = 95
F3  (1 )* F2   * A2 = (1.0 - 0.8)*95 + 0.8*110 = 107
F4 (1 )*F3   * A3 = (1.0 - 0.8)*107 + 0.8*163 = 151.80
etc.
F8  (1 )* F8   * A8 = (1.0 - 0.8)*173.44 + 0.8*183 = 181.09
SG7-4
15.00
56.00
-4.80
24.04
7.81
9.56
Chapter 7 Study Guide Solutions
SG7-5
Chapter 7 Study Guide Solutions
Problem 8
The number of girls who attend a summer basketball camp has been recorded for the
seven years the camp has been offered. Use exponential smoothing with a smoothing
constant of 0.8 to calculate the mean square error. The number of girls attending camp is:
95, 110, 163, 147, 172, 175, 183.
n
Mean Square Error =
MSE 
 (Y  Ŷ )
t 1
t
2
t
n
The Mean Square Error
685.73
Problem 9
Quarterly billing for water usage is shown below.
Seasonal Irregular
Component Values
Winter 0.971, 0.918. 0.908
Spring 0.840, 0.839, 0.834
Summer 1.096, 1.075, 1.109
Fall
1.133, 1.156, 1.141
What is the seasonal index for the Spring season?
Spring Seasonal Index = (0.840+0.839+0.834)/3 = 0.838
Problem 10
Quarterly billing for water usage is shown below.
Seasonal Irregular
Component Values
Winter 0.971, 0.918. 0.908
Spring 0.840, 0.839, 0.834
Summer 1.096, 1.075, 1.109
Fall
1.133, 1.156, 1.141
Seasonal
Indexes
0.93
0.84
1.09
1.14
Given the above information and new Winter sales number of 100, what is the
deseasonalized sales forecast?
Winter Deseasonalized Forecast = 100/0.93 = 107.52
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