Question

For a given data group, simple exponential smoothing is being used to forecast demand. The forecast of a given period is 110, which turned out to be 4 units more than actual demand. The forecast for next period is 109.2. Based on information given, what is smoothing constant, alpha? Select one:
a. 0.20
b. 0.10
c. 0.15
d. None of the choices
e. 0.60

Answer 1

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:

$s_t=\alpha x_t+(1-\alpha)s_{t-1}$

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:

$s_t=\alpha x_t+(1-\alpha)s_{t-1}\\\\109.2=\alpha*106+(1-\alpha)*110\\\\109.2=(106-110)\alpha+110\\\\(110-106)\alpha=110-109.2=0.8\\\\4\alpha=0.8\\\\\alpha=0.2$

Answer 2

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