Learning Outcomes
• Mahasiswa akan dapat menghubungkan masalah
aplikasi ramalan dengan berbagai metoda yang ada.
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Outline Materi:
•
•
•
•
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Moving Average
Eksponesial trend
Regression trend
Contoh ..
Moving Average Method
•
MA is a series of arithmetic means.
•
Used if little or no trend.
•
Used often for smoothing.
Demand in previous n periods

MA 
n
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Moving Average Example
You’re manager of a museum store that sells historical
replicas. You want to forecast sales (in thousands) for
months 4 and 5 using a 3-period moving average.
Month 1
Month 2
Month 3
Month 4
Month 5
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4
6
5
?
?
Moving Average Forecast
Month
1
2
3
4
5
6
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Response
Yi
4
6
5
?
?
?
Moving
Total
(n=3)
NA
NA
NA
4+6+5=15
Moving
Average
(n=3)
NA
NA
NA
15/3=5
Actual Demand for Month 4 = 3
Month
1
2
3
4
5
6
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Response
Yi
4
6
5
3
?
?
Moving
Total
(n=3)
NA
NA
NA
4+6+5=15
Moving
Average
(n=3)
NA
NA
NA
15/3 = 5
Moving Average Forecast
Month Response
Moving
Moving
Yi
Total
Average
(n=3)
(n=3)
1
4
NA
NA
2
6
NA
NA
3
5
NA
NA
15
5
4
3
5
7
6+5+3=14 14/3=4.667
6
?
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Actual Demand for Month 5 = 7
Month Response
Moving
Moving
Yi
Total
Average
(n=3)
(n=3)
1
4
NA
NA
2
6
NA
NA
3
5
NA
NA
15
4
3
5
5
7
6+5+3=14 14/3=4.667
6
?
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Moving Average Forecasts
Month Response
Moving
Moving
Yi
Total
Average
(n=3)
(n=3)
1
4
NA
NA
2
6
NA
NA
3
5
NA
NA
4
3
4+6+5=15 15/3=5.0
5
7
6+5+3=14 14/3=4.667
6
5+3+7=15 15/3=5.0
?
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Weighted Moving Average Method
• Gives more emphasis to recent data.
• Weights decrease for older data.
• Weights sum to 1.0.
– May be based on intuition.
– Sum of digits weights: numerators are consecutive.
• 3/6, 2/6, 1/6
• 4/10, 3/10, 2/10, 1/10
WMA =
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Σ [(Weight for period n) (Demand in period n)]
ΣWeights
Weighted Moving Average: 3/6, 2/6, 1/6
Month
1
2
3
4
5
6
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Response
Yi
4
6
5
?
?
?
Weighted
Moving
Average
NA
NA
NA
31/6 = 5.167
Weighted Moving Average: 3/6, 2/6, 1/6
Month
1
2
3
4
5
6
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Response
Yi
4
6
5
3
7
?
Weighted
Moving
Average
NA
NA
NA
31/6 = 5.167
25/6 = 4.167
32/6 = 5.333
Moving Average Methods
• Increasing n makes forecast:
– Less sensitive to changes.
– Less sensitive to recent data.
• Weights control emphasis on recent data.
• Do not forecast trend well.
• Require historical data.
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Exponential Smoothing Method
• Form of weighted moving average.
– Weights decline exponentially.
– Most recent data weighted most.
• Requires smoothing constant ().
– Usually ranges from 0.05 to 0.5
– Should be chosen to give good forecast.
• Involves little record keeping of past data.
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Exponential Smoothing Equation
•
Ft
= Ft-1 + (At-1 - Ft-1)
– Ft = Forecast value for time t
– At-1 = Actual value at time t-1
  = Smoothing constant
•
Need initial forecast Ft-1 to start.
– Could be given or use moving average.
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Exponential Smoothing Example
You want to forecast product demand using exponential smoothing
with  = .10. Suppose in the most recent month (month 6) the
forecast was 175 and the actual demand was 180.
Month 6
Month 7
Month 8
Month 9
Month 10
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180
?
?
?
?
Exponential Smoothing - Month 7
Month
Actual
6
180
7
?
8
?
9
?
10
?
11
?
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Forecast, F t
(α = .10)
175.00 (Given)
175.00 + .10(180 - 175.00) = 175.50
Ft = Ft-1 + α (At-1 - Ft-1)
Exponential Smoothing - Month 8
Forecast, F t
(α = .10)
Month
Actual
6
180
7
168
175.00 + .10(180 - 175.00) = 175.50
8
?
175.50 + .10(168 - 175.50) = 174.75
9
?
10
?
11
?
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175.00 (Given)
Ft = Ft-1 + α (At-1 - Ft-1)
Exponential Smoothing Solution
Forecast, F t
(α = .10)
Month
Actual
6
180
7
168
175.00 + .10(180 - 175.00) = 175.50
8
159
175.50 + .10(168 - 175.50) = 174.75
9
?
174.75 + .10(159 - 174.75) = 173.18
10
?
11
?
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175.00 (Given)
Ft = Ft-1 + α (At-1 - Ft-1)
Exponential Smoothing Solution
Forecast, F t
(α = .10)
Month
Actual
6
180
7
168
175.00 + .10(180 - 175.00) = 175.50
8
159
175.50 + .10(168 - 175.50) = 174.75
9
175
174.75 + .10(159 - 174.75) = 173.18
10
190
173.18 + .10(175 - 173.18) = 173.36
11
?
173.36 + .10(190 - 173.36) = 175.02
175.00 (Given)
Ft = Ft-1 + α (At-1 - Ft-1)
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Exponential Smoothing Methods
• Increasing α makes forecast:
– More sensitive to changes.
– More sensitive to recent data.
• α controls emphasis on recent data.
• Do not forecast trend well.
– Trend adjusted exponential smoothing - p. 90-93
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Forecast Effects of
Smoothing Constant 
Ft =  At - 1 + (1- )At - 2 + (1- )2At - 3 + ...
Weights
=
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Prior Period
2 periods ago 3 periods ago

(1 - )
(1 - )2
= 0.10
10%
9%
8.1%
= 0.90
90%
9%
0.9%
Choosing  - Comparing Forecasts
A good method has a small error.
Choose  to produce a small error.
 Error = Demand - Forecast
Error > 0 if forecast is too low
Error < 0 if forecast is too high
MAD = Mean Absolute Deviation: Average of absolute
values of errors.
MSE = Mean Squared Error: Average of squared errors.
MAPE = Mean Absolute Percentage Error: Average of
absolute value of percentage errors.
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Forecast Error Equations
• Mean Absolute Deviation (MAD)
n
MAD 
| yi  yˆ i |
i1
n
| forecast errors |


n
• Mean Squared Error (MSE)
n
MSE 
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 (y i  yˆ i )2
i1
n
forecast errors


n
2
Forecast Error Equations
• Mean Absolute Percentage Error (MAPE)
| y i  yˆ i |
| forecast errors |


yi
i1
Actual
MAPE 

n
n
n
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Forecast Error Example
Actual
20
10
24
20
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F1
19
15
22
21
F1 error
1
-5
2
-1
F2
18
13
21
18
F2 error
2
-3
3
2
MAD
F1 = 9/4 = 2.25
F2 = 10/4 = 2.5
MSE
F1 = 31/4 = 7.75
F2 = 26/4 = 6.5
MAPE
F1 = 0.171 = 17.1%
F2 = 0.156 = 15.6%
Which Forecast is Best?
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MAD
F1 = 9/4 = 2.25
F2 = 10/4 = 2.5
MSE
F1 = 31/4 = 7.75
F2 = 26/4 = 6.5
MAPE
F1 = 0.171 = 17.1%
F2 = 0.156 = 15.6%
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