Page 96 - DMGT523_LOGISTICS_AND_SUPPLY_CHAIN_MANAGEMENT

Unit 4: Demand Planning and Forecasting

(D – F )² i.e. Total Variance when  = 0.2 is 69.98 [Col. 6] Notes
t t–1
Therefore,
Error Variance of the series = (D – F )²/(n – 1) = 69.98/9 = 7.75
t t–1
Similarly, (D – F )² i.e. Total Variance with  = 0.5 is 42.38 [Col. 10]
t t–1
Therefore,
Error Variance of the series = (D – F )²/(n – 1) = 42.38/9 = 4.70
t t–1
Where 'n' is the number of observations.
One measure of the accuracy of the forecast is the error variance, which is the mean squared
error between the forecast and the actual data in the next period [ (D – F )²/(n – 1)] which has
t t–1
been calculated above. You have to pick the  that gives you the smallest mean squared error or
error variance.
Since the error variance for the case of  = 0.2 is greater than for  = 0.5, the forecast with  = 0.5
is the correct choice as it is more accurate.
Simple Moving Average and Exponentially Weighted Moving Average: An exponentially
weighted moving average with a smoothing constant ' ', roughly corresponds to a simple
moving average period of length 'n', where ' ' and 'n' are related by the following equation:
= 2/(n + 1) OR n = (2 – )/ .
Therefore, an exponentially weighted moving average with a smoothing constant equal to 0.1
would roughly correspond to a 19 day moving average. Similarly, a 40-day simple moving
average would correspond roughly to an exponentially weighted moving average with a
smoothing constant equal to 0.04878. These values are based on the equations given above.
This goes to show that 'simple moving average' is a special case of exponential smoothing. The
forecasts generated by exponential smoothing have the same average age as a moving average
of order 'n' such that the integer part is (2 - )/ .
Double Exponential Smoothing: An exponential smoothing over an already smoothed time
series is called double-exponential smoothing. Double exponential smoothing allows forecasting
data with trends. While the single exponential method is used for problems where the trends are
stationary, the double exponential method is used to handle trends that are not stationary.
By exponentially smoothening a smoothened series again, a linear trend in the forecasted value
is obtained. The extrapolated series has a constant growth rate, equal to the growth of the
smoothed series at the end of the data period.
Triple Double Exponential Smoothing: When the trends are non-linear, it may be necessary to
extend it even to a triple-exponential smoothing. Triple Exponential Smoothing is better at
handling parabola trends and is normally used for such data.

While simple exponential smoothing requires stationary conditions in the demand parameters,
the double-exponential smoothing can capture trends when the demand is changing in a linear
fashion. Triple-exponential smoothing can be used to handle almost all other business time
series.
The advantages of exponential smoothing are that it does not impose any deterministic model
to fit the series other than what is inherent in the time series itself. It can be modified to capture
seasonal patterns for a time series. Whereas moving averages provide for equal weights for past
observations, exponential smoothing assigns exponentially decreasing weights as the
observation gets older.

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