Operations and Supply Chain Management The Core

56 OPERATIONS AND SUPPLY CHAIN MANAGEMENT
where
F t = The exponentially smoothed forecast that does not include trend for period t
T t = The exponentially smoothed trend for period t
FIT t = The forecast including trend for period t
FIT t−1 = The forecast including trend made for the prior period
A t−1 = The actual demand for the prior period
α = Smoothing constant (alpha)
δ = Smoothing constant (delta)
To make an exponential forecast that includes trend, step through the equations one at a
time.
Step 1: Using equation 3.4, make a forecast that is not adjusted for trend. This uses
the previous forecast and previous actual demand.
Step 2:
Using equation 3.5, update the estimate of trend using the previous trend estimate,
the unadjusted forecast just made, and the previous forecast.
Step 3: Make a new forecast that includes trend by using the results from steps 1
and 2.
Example 3.1: Forecast Including Trend
Assume a previous forecast including trend of 110 units, a previous trend estimate of 10 units, an
alpha of 0.20, and a delta of 0.30. If actual demand turned out to be 115 rather than the forecast 110,
calculate the forecast for the next period.
SOLUTION
The actual A t−1 is given as 115. Therefore,
​
​F​ t ​=
​FIT​ t−1 ​ + α(​A​ t−1 ​ − ​FIT​ t−1 ​)
​=
110 + 0.2(115 − 110) = 111.0
​T​ t ​ =​ ​T​ t−1 ​ + δ(​F​ t ​ − ​FIT​ t−1 ​)​ ​ ​ ​ ​
​=
10 + 0.3(111 − 110) = 10.3
​FIT​ t ​=
​F​ t ​ + ​T​ t ​ = 111.0 + 10.3 = 121.3
If, instead of 121.3, the actual turned out to be 120, the sequence would be repeated and the forecast
for the next period would be
​F​ t+1 ​=
121.3 + 0.2(120 − 121.3) = 121.04
​ ​T​ t+1 ​
=​ 10.3 + 0.3(121.04 − 121.3) = 10.22​ ​
​FIT​ t+1 ​=
121.04 + 10.22 = 131.26
•
Choosing the Appropriate Value for Alpha and Delta Exponential smoothing
requires that the smoothing constants be given a value between 0 and 1. Typically, fairly
small values are used for alpha and delta in the range of 0.1 to 0.3. The values depend on
how much random variation there is in demand and how steady the trend factor is. Later in