ISEN 220 Introduction to Production and Manufacturing Systems

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ISEN 220Introduction to Production and
Manufacturing Systems
11/20/2009
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Texas AM Industrial Engineering
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Graph of Moving Average
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Potential Problems With Moving Average

• Increasing n smooths the forecast but makes it
  less sensitive to changes
• Do not forecast trends well
• Require extensive historical data

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Exponential Smoothing

• Form of weighted moving average
• Weights decline exponentially
• Most recent data weighted most
• Requires smoothing constant (?)
• Ranges from 0 to 1
• Subjectively chosen
• Involves little record keeping of past data

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Exponential Smoothing
New forecast last periods forecast a (last
periods actual demand last periods
forecast)
Ft Ft 1 a(At 1 - Ft 1)
where Ft new forecast Ft 1 previous
forecast a smoothing (or weighting)
constant (0 ? a ? 1)
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Exponential Smoothing Example
Predicted demand 142 Ford Mustangs Actual
demand 153 Smoothing constant a .20
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Effect of Smoothing Constants
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Effect of Smoothing Constants
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Effect of Smoothing Constants
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Impact of Different ?
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Choosing ?
The objective is to obtain the most accurate
forecast no matter the technique
We generally do this by selecting the model that
gives us the lowest forecast error
Forecast error Actual demand - Forecast
value At - Ft
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Choosing ?
Can forecast historic data and compare to
actuals
Then select the parameter value that gives us the
lowest forecast error
This method inherently assumes that the future
is going to be similar to the past
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Common Measures of Error
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Common Measures of Error
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Comparison of Forecast Error
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Comparison of Forecast Error
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Comparison of Forecast Error
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Comparison of Forecast Error
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Comparison of Forecast Error
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Exponential Smoothing with Trend Adjustment
When a trend is present, exponential smoothing
must be modified
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Exponential Smoothing with Trend Adjustment
Ft a(At - 1) (1 - a)(Ft - 1 Tt - 1)
Tt b(Ft - Ft - 1) (1 - b)Tt - 1
Step 1 Compute Ft Step 2 Compute Tt Step 3
Calculate the forecast FITt Ft Tt
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Exponential Smoothing with Trend Adjustment
Example
Table 4.1
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Exponential Smoothing with Trend Adjustment
Example
Step 1 Forecast for Month 2
F2 aA1 (1 - a)(F1 T1) F2
Table 4.1
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Exponential Smoothing with Trend Adjustment
Example
Step 2 Trend for Month 2
T2 b(F2 - F1) (1 - b)T1 T2
Table 4.1
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Exponential Smoothing with Trend Adjustment
Example
Step 3 Calculate FIT for Month 2
FIT2 F2 T1 FIT2
Table 4.1
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Exponential Smoothing with Trend Adjustment
Example
15.18 2.10 17.28 17.82 2.32 20.14 19.91
2.23 22.14 22.51 2.38 24.89 24.11 2.07 26.18
27.14 2.45 29.59 29.28 2.32 31.60 32.48
2.68 35.16
Table 4.1
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Exponential Smoothing with Trend Adjustment
Example
Figure 4.3