Simple exponential smoothing is being used to forecast demand. The previous forecast of 66 turned out to be four units less than actual demand. The next forecast is 66.6, implying alpha equal to:
(A) 0.15
(B) 0.01
(C) 0.20
(D) 0.10
(E) 0.60
Answer (1)
To solve this problem, we need to understand how simple exponential smoothing works in forecasting.
Simple Exponential Smoothing Formula
The formula for simple exponential smoothing is:
F t + 1 = α × A t + ( 1 − α ) × F t
Where:
F t + 1 is the next forecast.
α is the smoothing constant.
A t is the actual demand at time t .
F t is the forecast for time t .
Step-by-Step Solution
Given Values :
Previous forecast F t = 66 .
Actual demand A t = 66 + 4 = 70 (since the forecast was 4 units less).
Next forecast F t + 1 = 66.6 .
Substitute in the Formula :
66.6 = α × 70 + ( 1 − α ) × 66
Solve for α :
Expand and solve the equation:
66.6 = 70 α + 66 − 66 α
66.6 = 70 α − 66 α + 66
66.6 = 4 α + 66
Subtract 66 from both sides:
0.6 = 4 α
Divide by 4:
α = 0.15
Thus, the smoothing constant α is 0.15.
The correct answer is option (A) 0.15.
