Answer:
The smoothing constant alpha is 0.20 (Option a)
Step-by-step explanation:
To solve this problem, first we write the succession of the simple exponential smoothing:
[tex]s_t=\alpha x_t+(1-\alpha)s_{t-1}[/tex]
Where s(t) is the forecast for period t, s(t-1) is the forecast for period (t-1), xt is the real demand for period t, and alpha is the smoothing constant.
All but the alpha constant are known
s(t)=109.2
s(t-2)=110
xt=110-4=106
Then, we can calculate alpha as:
[tex]s_t=\alpha x_t+(1-\alpha)s_{t-1}\\\\109.2=\alpha*106+(1-\alpha)*110\\\\109.2=(106-110)\alpha+110\\\\(110-106)\alpha=110-109.2=0.8\\\\4\alpha=0.8\\\\\alpha=0.2[/tex]
Answer:
a. 0.20
Step-by-step explanation:
To obtain the smoothing constant, alpha; we consider the formula;
Ŷt+1 = αYt + (1-α) Ŷt
In this equation, Ŷt+1 represents the forecast value for period t + 1; Yt is the actual value of the current period, t; Ŷt is the forecast value for the current period, t; and α is the smoothing constant, or alpha, a number between 0 and 1
Therefore, as given.:
Ŷt+1 = 109.2 Yt = 106
Ŷt = 110 α = ?
Hence, substituting into the formula we have,
109.2 = α(106) + (1 - α)110
: 109.2 = α(106) +110 - α110
: - 0.8 = - 4α
∴α = 0.2
