National Scan, Inc., sells radio frequency inventory tags. Monthly sales for a seven­month period were as follows:

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1. Award: 25 out of 25.00 points
Score: 100/100 Points 100 %
Problem 3-2
National Scan, Inc., sells radio frequency inventory tags. Monthly sales for a seven­month period were as
follows:
Month
Sales
(000)Units
Feb. 19
Mar. 18
Apr. 15
May 20
Jun. 18
Jul. 22
Aug. 20
b. Forecast September sales volume using each of the following:
(1) A linear trend equation. (Round your intermediate calculations and final answer to 2 decimal
places.)
Yt 20.86 thousands
(2) A five­month moving average.
Moving average 19 thousands
(3) Exponential smoothing with a smoothing constant equal to .20, assuming a March forecast of
19(000). (Round your intermediate calculations and final answer to 2 decimal places.)
Forecast 19.26 thousands
(4) The naive approach.
Naive approach 20 thousands
(5) A weighted average using .60 for August, .30 for July, and .10 for June. (Round your answer to 2
decimal places.)
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Weighted average 20.40 thousands
References
Worksheet Learning Objective:
03­07 Use a naive
method to make a
forecast.
Learning Objective: 03­10 Prepare an
exponential smoothing forecast.
Problem 3­2 Learning Objective:
03­08 Prepare a
moving average
forecast.
Problem 3-2
National Scan, Inc., sells radio frequency inventory tags. Monthly sales for a seven­month period were as
follows:
Month
Sales
(000)Units
Feb. 19
Mar. 18
Apr. 15
May 20
Jun. 18
Jul. 22
Aug. 20
b. Forecast September sales volume using each of the following:
(1) A linear trend equation. (Round your intermediate calculations and final answer to 2 decimal
places.)
Yt
20.86 ± 0.10 thousands
(2) A five­month moving average.
Moving average 19 thousands
(3) Exponential smoothing with a smoothing constant equal to .20, assuming a March forecast of
19(000). (Round your intermediate calculations and final answer to 2 decimal places.)
Forecast
19.26 ± 0.10
thousands
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2. Award: 25 out of 25.00 points
(4) The naive approach.
Naive approach 20 thousands
(5) A weighted average using .60 for August, .30 for July, and .10 for June. (Round your answer to 2
decimal places.)
Weighted average
20.40 ± 0.01
thousands
Explanation:
b.
(1)
t Y tY
1 19 19
2 18 36
3 15 45
4 20 80
5 18 90
6 22 132
7 20 140
28 132 542
with n = 7, Σt = 28, Σt
2 = 140
b =
nΣty − ΣtΣy
=
7(542) − 28(132)
= .50
nΣt
2 − (Σt)
2 7(140) − 28(28)
a =
Σy − bΣt
=
132 − .50(28)
= 16.86
n 7
For Sept., t = 8, and Yt = 16.86 + .50(8) = 20.86 (000)
(2)
MA5 =
15 + 20 + 18 + 22 + 20
= 19
5
(3)
Month Forecast = F(old) + .20 [Actual − F(Old)]
April 18.8 = 19 + .20 [18 − 19]
May 18.04 = 18.8 + .20 [15 − 18.8]
June 18.43 = 18.04 + .20 [20 − 18.04]
July 18.34 = 18.43 + .20 [18 − 18.43]
August 19.07 = 18.34 + .20 [22 − 18.34]
September 19.26 = 19.07 + .20 [20 − 19.07]
(5)
.60(20) + .30(22) + .10(18) = 20.40
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Problem 3-3
A dry cleaner uses exponential smoothing to forecast equipment usage at its main plant. August usage
was forecasted to be 88 percent of capacity; actual usage was 89.6 percent of capacity. A smoothing
constant of .1 is used.
a. Prepare a forecast for September. (Round your answer to 2 decimal places.)
Forecast for September 88.16 percent of capacity
b. Assuming actual September usage of 92 percent, prepare a forecast for October usage.(Round your
answer to 2 decimal places.)
Forecast for October 88.54 percent of capacity
References
Worksheet Problem 3­3 Learning Objective: 03­10 Prepare an
exponential smoothing forecast.
Problem 3-3
A dry cleaner uses exponential smoothing to forecast equipment usage at its main plant. August usage
was forecasted to be 88 percent of capacity; actual usage was 89.6 percent of capacity. A smoothing
constant of .1 is used.
a. Prepare a forecast for September. (Round your answer to 2 decimal places.)
Forecast for September 88.16 ± 0.05 percent of capacity
b. Assuming actual September usage of 92 percent, prepare a forecast for October usage.(Round your
answer to 2 decimal places.)
Forecast for October 88.54 ± 0.05 percent of capacity
Explanation:
a.
88 + .1(89.6 − 88) = 88.16
b.
88.16 + .1(92 − 88.16) = 88.54
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3. Award: 25 out of 25.00 points
Problem 3-4
An electrical contractor’s records during the last five weeks indicate the number of job requests:
Week: 1 2 3 4 5
Requests: 20 22 18 21 22
Predict the number of requests for week 6 using each of these methods:
a. Naive.
Number of requests 22
b. A four­period moving average. (Round your answer to 2 decimal places.)
Number of requests 20.75
c. Exponential smoothing with α = .30. Use 20 for week 2 forecast. (Round your intermediate
calculations and final answers to 2 decimal places.)
Number of Requests
F3 20.6
F4 19.82
F5 20.17
F6 20.72
References
Worksheet Learning Objective:
03­07 Use a naive
method to make a
forecast.
Learning Objective: 03­10 Prepare an
exponential smoothing forecast.
Problem 3­4 Learning Objective:
03­08 Prepare a
moving average
forecast.
Problem 3-4
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4. Award: 25 out of 25.00 points
An electrical contractor’s records during the last five weeks indicate the number of job requests:
Week: 1 2 3 4 5
Requests: 20 22 18 21 22
Predict the number of requests for week 6 using each of these methods:
a. Naive.
Number of requests 22
b. A four­period moving average. (Round your answer to 2 decimal places.)
Number of requests 20.75 ± 0.01
c. Exponential smoothing with α = .30. Use 20 for week 2 forecast. (Round your intermediate
calculations and final answers to 2 decimal places.)
Number of Requests
F3 20.6 ± 0.05
F4 19.82 ± 0.05
F5 20.17 ± 0.05
F6 20.72 ± 0.05
Explanation:
b.
22 + 18 + 21 + 22
= 20.75
4
c.
F3 = 20 + .30(22 − 20) = 20.6
F4 = 20.6 + .30(18 − 20.6) = 19.82
F5 = 19.82 + .30(21 − 19.82) = 20.17
F6 = 20.17 + .30(22 − 20.17) = 20.72
Problem 3-32
A manager has just received an evaluation from an analyst on two potential forecasting alternatives. The
analyst is indifferent between the two alternatives, saying that they should be equally effective.
Period: 1 2 3 4 5 6 7 8 9 10
Data: 37 39 37 39 45 49 47 49 51 54
Alt. 1: 36 38 40 42 46 46 46 48 52 55
Alt. 2: 36 37 38 38 41 52 47 48 52 53
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What would cause the analyst to reach this conclusion? (Round your answers to 2 decimal places.)
MAD1 1.60
MAD2 1.50
MSE1 3.78
MSE2 3.89
rev: 11_18_2014_QC_59428
References
Worksheet Learning Objective:
03­15 Construct
control charts and
use them to monitor
forecast errors.
Problem 3­32 Learning Objective:
03­16 Describe the
key factors and
trade­offs to
consider when
choosing a
forecasting
technique.
Problem 3-32
A manager has just received an evaluation from an analyst on two potential forecasting alternatives. The
analyst is indifferent between the two alternatives, saying that they should be equally effective.
Period: 1 2 3 4 5 6 7 8 9 10
Data: 37 39 37 39 45 49 47 49 51 54
Alt. 1: 36 38 40 42 46 46 46 48 52 55
Alt. 2: 36 37 38 38 41 52 47 48 52 53
What would cause the analyst to reach this conclusion? (Round your answers to 2 decimal places.)
MAD1 1.60 ± 0.05
MAD2 1.50 ± 0.05
MSE1 3.78 ± 0.05
MSE2 3.89 ± 0.05
rev: 11_18_2014_QC_59428
Explanation:
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Period Actual Forecast 1 Forecast 2 error 1 error 2 e1
2
e2
2 |e1| |e2|
1 37 36 36 +1 +1 1 1 1 1
2 39 38 37 +1 +2 1 4 1 2
3 37 40 38 –3 –1 9 1 3 1
4 39 42 38 –3 +1 9 1 3 1
5 45 46 41 –1 +4 1 16 1 4
6 49 46 52 +3 –3 9 9 3 3
7 47 46 47 1 0 1 0 1 0
8 49 48 48 1 +1 1 1 1 1
9 51 52 52 –1 –1 1 1 1 1
10 54 55 53 –1 +1 1 1 1 1
Total –2 +5 34 35 16 15
MSE1 =
34
= 3.78
9
MSE2 =
35
= 3.89
9
MAD1 =
16
= 1.6
10
MAD2 =
15
= 1.5
10
Both forecasting methods have MADs that are approximately equal (MAD1 = 1.6, MAD2 = 1.5), and MSEs
that are also approximately equal (MSE1 = 3.78, MSE2 = 3.89).

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