Operations and Supply Chain Management The Core

FORECASTING chapter 3 55
Exponential Forecasts versus Actual Demand for Units of a
Product over Time Showing the Forecast Lag
exhibit 3.5
500
400
300
F t = F t–1 + α(A t–1 – F t–1 )
α = 0.1, 0.3, and 0.5
α = 0.5
α = 0.3
Actual
200
α = 0.1
100
0
J
F
M
A
M
J
J
A
S
O
N
D
J
F
M
A
M
J
J
A
S
O
N
D
J
F
be added. Adjusting the value of alpha also helps. This is termed adaptive forecasting.
Both trend effects and adaptive forecasting are briefly explained in the following sections.
Exponential Smoothing with Trend
Remember that an upward or downward trend in data collected over a sequence of time
periods causes the exponential forecast to always lag behind (be above or below) the actual
occurrence. Exponentially smoothed forecasts can be corrected somewhat by adding in
a trend adjustment. To correct the trend, we need two smoothing constants. Besides the
smoothing constant α, the trend equation also uses a smoothing constant delta (δ). Both
alpha and delta reduce the impact of the error that occurs between the actual and the forecast.
If both alpha and delta are not included, the trend overreacts to errors.
To get the trend equation going, the first time it is used the trend value must be entered
manually. This initial trend value can be an educated guess or a computation based on
observed past data.
The equations to compute the forecast including trend (FIT) are
Smoothing constant
delta (δ)
An additional
parameter used
in an exponential
smoothing equation
that includes an
adjustment for trend.
​F​ t ​ = ​FIT​ t−1 ​ + α(​A​ t−1 ​ − ​FIT​ t−1 ​)​ [3.4]
​T​ t ​ = ​T​ t−1 ​ + δ(​F​ t ​ − ​FIT​ t−1 ​)​ [3.5]
​FIT​ t ​ = ​F​ t ​ + ​T​ t ​ [3.6]