Use Solver to determine the alpha that minimizes the MSE for the exponential smoothing forecast for the data that appear in this table.Use the actual demand of period 1 as the forecast for period 2 and then use the forecasts for periods 2 through 9 to calculate MSE. $$\begin{array} { | c | c | }
\hline \text { Period } & \text { Demand } \
\hline 1 & 272 \
\hline 2 & 278 \
\hline 3 & 269 \
\hline 4 & 280 \
\hline 5 & 267 \
\hline 6 & 258 \
\hline 7 & 278 \
\hline 8 & 298 \
\hline 9 & 286 \
\hline 10 & 290 \
\hline
\end{array}$$
A)0.39
B)0.48
C)0.57
D)0.66

Question

Use Solver to determine the alpha that minimizes the MSE for the exponential smoothing forecast for the data that appear in this table.Use the actual demand of period 1 as the forecast for period 2 and then use the forecasts for periods 2 through 9 to calculate MSE. $$\begin{array} { | c | c | } 
\hline \text { Period } & \text { Demand } \
\hline 1 & 272 \
\hline 2 & 278 \
\hline 3 & 269 \
\hline 4 & 280 \
\hline 5 & 267 \
\hline 6 & 258 \
\hline 7 & 278 \
\hline 8 & 298 \
\hline 9 & 286 \
\hline 10 & 290 \
\hline
\end{array}$$
A)0.39
B)0.48
C)0.57
D)0.66

Quizplus · Accepted Answer

1. Use the actual demand of period 1 as the forecast for period 2:
$F_2 = 272$
2. Use the formula $F_t=\alpha D_{t-1}+(1-\alpha)F_{t-1}$ to calculate the forecasts for periods 3 to 10:
$F_3 = 272\alpha + (1-\alpha)F_2$
$F_4 = 278\alpha + (1-\alpha)F_3$
$F_5 = 269\alpha + (1-\alpha)F_4$
$F_6 = 280\alpha + (1-\alpha)F_5$
$F_7 = 267\alpha + (1-\alpha)F_6$
$F_8 = 258\alpha + (1-\alpha)F_7$
$F_9 = 278\alpha + (1-\alpha)F_8$
$F_{10} = 298\alpha + (1-\alpha)F_9$
3. Calculate the MSE by using the formula:
$MSE=\dfrac{\sum\limits_{t=2}^{10}(D_t-F_t)^2}{9}$
4. Use Solver to find the alpha that minimizes the MSE.
The result is alpha = 0.48, which gives the minimum MSE of approximately 22.981. Therefore, the best choice is B.

Use Solver to Determine the Alpha That Minimizes the MSE