Forecast method: exponential smoothing
LN calculates the demand forecast according to the Exponential Smoothing forecast method as follows:
The relevant parameters for this forecast method are:
- Automatic Update of Forecast Parameters
- Smoothing Factor for Demand
- Smoothing Factor for Trend
- Smoothing Factor for Season
- Smoothing Factor for Forecast Error
- Tracking Signal for Demand Forecast
- Critical Tracking Signal
You can maintain these parameters in the Plan Items - Forecast Settings (cpdsp1110m000) session.
If the Automatic Update of Forecast Parameters check box is selected, LN first recomputes the smoothing factors for the exponential smoothing method. Using an iterative process, with step sizes of 0.2 and subsequently 0.05, LN produces an optimum combination of smoothing factors for the demand, the season, and the trend. This combination gives the smallest mean absolute deviation (MAD).
Next, LN calculates a demand forecast starting from the first period with demand history to the last forecast period via the exponential smoothing method.
The various variables for the demand forecast are computed as follows:
Average demand
Without seasonal influence:
AV(t) = FD(t) + a (AD(t) - FD(t))With a constant seasonal influence:
AV(t) = (FD(t) + a (AD(t) - FD(t))) - SF(t)With a progressive seasonal influence:
AV(t) = (FD(t) + a (AD(t) - FD(t))) / SF(t)Where:
| AV(t) | season-adjusted average demand for period t |
| FD(t) | demand forecast for period t |
| AD(t) | actual demand for period t (*) |
| SF(t) | seasonal factor for period t |
| a | Smoothing Factor for Demand field |
(*) For the current period and later periods, the forecast demand is taken as the actual demand.
Trend factor
With a linear trend influence:
TF(t) = TF(t-1) + b ((AV(t)-AV(t-1)) - TF(t-1))With a progressive trend influence:
TF(t) = TF(t-1) + b (1.0 + ((AV(t)-AV(t-1))/AV(t)) - TF(t-1))Where:
| TF(t) | trend factor for period t |
| AV(t) | season-adjusted average demand for period t |
| b | Smoothing Factor for Trend field |
Seasonal factor
With a constant seasonal influence:
SF(t+L) = SF(t) + g ((AD(t) - AV(t)) - SF(t))With a progressive seasonal influence:
SF(t+L) = SF(t) + g ((AD(t) / AV(t)) - SF(t))Where:
| SF(t) | seasonal factor for period t |
| AD(t) | actual demand for period t (*) |
| AV(t) | season-adjusted average demand for period t |
| L | season length in periods |
| g | Smoothing Factor for Season field |
(*) For the current period and later periods, the forecast demand is taken as the actual demand.
Demand forecast
Without trend influence:
FD(t+1) = AV(t)With a linear trend influence:
FD(t+1) = FD(t+1) + TF(t)With a progressive trend influence:
FD(t+1) = FD(t+1) * TF(t)With a constant seasonal influence:
FD(t+1) = FD(t+1) + SF(t+1)With a progressive seasonal influence:
FD(t+1) = FD(t+1) * SF(t+1)Where:
| AV(t) | season-adjusted average demand for period t |
| TF(t) | trend factor for period t |
| SF(t+1) | seasonal factor for period t+1 |
| FD(t+1) | demand forecast for period t+1 |
Mean forecast error
Where:
| AD(t) | actual demand for period t |
| FD(t) | demand forecast for period t |
| AE(t) | mean absolute deviation (MAD) for period t |
| SE(t) | mean forecast error (SER) for period t |
| abs(FD(t)-AD(t)) | absolute value of (FD(t)-AD(t)) |
| e | Smoothing Factor for Forecast Error field |
The tracking signal is calculated as follows:
TS(t) = abs(SE(t)/AE(t)) Where:
| TS(t) | tracking signal |
| SE(t) | mean forecast error (SER) for period t |
| AE(t) | mean absolute deviation (MAD) for period t |
| abs(SE(t)/AE(t)) | absolute value of (SE(t)/AE(t)) |
If the forecast demand (FD) is always greater than the actual demand (AD), the value of (SE(t)/AE(t)) is 1. If the forecast demand (FD) is always less than the actual demand, the value of (SE(t)/AE(t)) is -1. The tracking signal is a number between 0 and 1. The tracking signal indicates whether the forecast demand is systematically above or below the actual demand.
If the Tracking Signal for Demand Forecast check box is selected, the smoothing factor for the demand is dependent on the forecast error.
If the tracking signal is greater than the value of the Critical Tracking Signal field, LN makes the smoothing factor for the demand equal to the tracking signal.