Example: Method 11: Exponential Smoothing

This method is similar to Method 10, Linear Smoothing. In Linear Smoothing, the system assigns weights that decline linearly to the historical data. In Exponential Smoothing, the system assigns weights that exponentially decay. The equation for Exponential Smoothing forecasting is:

Forecast = α (Previous Actual Sales) + (1 –α) (Previous Forecast)

The forecast is a weighted average of the actual sales from the previous period and the forecast from the previous period. Alpha is the weight that is applied to the actual sales for the previous period. (1 – α) is the weight that is applied to the forecast for the previous period. Values for alpha range from 0 to 1 and usually fall between 0.1 and 0.4. The sum of the weights is 1.00 (α + (1 – α) = 1).

You should assign a value for the smoothing constant, alpha. If you do not assign a value for the smoothing constant, the system calculates an assumed value that is based on the number of periods of sales history that is specified in the processing option.

Forecast specifications:

• α equals the smoothing constant that is used to calculate the smoothed average for the general level or magnitude of sales.

  Values for alpha range from 0 to 1.

• n equals the range of sales history data to include in the calculations.

  Generally, one year of sales history data is sufficient to estimate the general level of sales. For this example, a small value for n (n = 4) was chosen to reduce the manual calculations that are required to verify the results. Exponential Smoothing can generate a forecast that is based on as little as one historical data point.

Minimum required sales history: n plus the number of time periods that are required for evaluating the forecast performance (periods of best fit).

This table is history used in the forecast calculation:

Past Year	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
1	None	None	None	None	None	None	None	None	131	114	119	137

This table is the calculation of Exponential Smoothing, given n = 4, α = 0.3:

Month	Calculation
October Smoothed Average*	= September Actual = α (September Actual) + (1 –α) September Smoothed Average = 1 * (131) + (0) (0) = 131
November Smoothed Average	= 0.3 (October Actual) + (1 – 0.3) October Smoothed Average = 0.3 (114) + 0.7 (131) = 125.9 rounded to 126
December Smoothed Average	= 0.3 (November Actual) + 0.7 (November Smoothed Average) = 0.3 (119) + 0.7 (126) = 123.9 or 124
January Forecast	= 0.3 (December Actual) + 0.7 (December Smoothed Average) = 0.3 (137) + 0.7 (124) = 127.9 or 128
February Forecast	= January Forecast
March Forecast	= January Forecast

* Exponential Smoothing is initialized by setting the first smoothed average equal to the first specified actual sales data point. In effect, α = 1.0 for the first iteration. For subsequent calculations, alpha is set to the value that is specified in the processing option.

This table is the Exponential Smoothing forecast for next year, given α = 0.3, n = 4:

Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
128	128	128	128	128	128	128	128	128	128	128	128