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The following table shows the actual demand observed over the last 11 years:
[tex]\[
\begin{tabular}{lccccccccccc}
\hline
Year & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 \\
\hline
Demand & 6 & 10 & 6 & 9 & 13 & 7 & 12 & 13 & 8 & 11 & 7 \\
\hline
\end{tabular}
\][/tex]

Using exponential smoothing with [tex]$\alpha=0.30$[/tex] and a forecast for year 1 of 5.0, provide the forecast for periods 2 through 12 (round your responses to one decimal place):
[tex]\[
\begin{tabular}{lcccccccccccc}
\hline
Year & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 \\
\hline
Forecast & 5.0 & 5.3 & 6.7 & 6.8 & 7.3 & 9.0 & 8.1 & 9.5 & 10.6 & 9.8 & 10.5 & 9.2 \\
\hline
\end{tabular}
\][/tex]

Provide the forecast for periods 2 through 12 using the naive approach (enter your responses as whole numbers):
[tex]\[
\begin{tabular}{lccccccccccc}
\hline
Year & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 \\
\hline
Forecast & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ \\
\hline
\end{tabular}
\][/tex]

Sagot :

GinnyAnswer
To find the forecast for periods 2 through 12 using the naive approach, we use the actual demand of the previous period as the forecast for the next period. Here’s a step-by-step approach:

1. Year 2 Forecast: The forecast for year 2 is the actual demand of year 1.
2. Year 3 Forecast: The forecast for year 3 is the actual demand of year 2.
3. Year 4 Forecast: The forecast for year 4 is the actual demand of year 3.
4. Year 5 Forecast: The forecast for year 5 is the actual demand of year 4.
5. Year 6 Forecast: The forecast for year 6 is the actual demand of year 5.
6. Year 7 Forecast: The forecast for year 7 is the actual demand of year 6.
7. Year 8 Forecast: The forecast for year 8 is the actual demand of year 7.
8. Year 9 Forecast: The forecast for year 9 is the actual demand of year 8.
9. Year 10 Forecast: The forecast for year 10 is the actual demand of year 9.
10. Year 11 Forecast: The forecast for year 11 is the actual demand of year 10.
11. Year 12 Forecast: The forecast for year 12 is the actual demand of year 11.

Given the actual demand data:
[tex]\[ \begin{array}{|c|ccccccccccc|} \hline \text{Year} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 \\ \hline \text{Demand} & 6 & 10 & 6 & 9 & 13 & 7 & 12 & 13 & 8 & 11 & 7 \\ \hline \end{array} \][/tex]

Using the naive approach, the forecast values are calculated as follows:
[tex]\[ \begin{array}{|c|ccccccccccc|} \hline \text{Year} & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 \\ \hline \text{Forecast} & 10 & 6 & 9 & 13 & 7 & 12 & 13 & 8 & 11 & 7 \\ \hline \end{array} \][/tex]

Therefore, the forecast from periods 2 through 12 is:
[tex]\[ \begin{array}{|c|ccccccccccc|} \hline \text{Year} & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 \\ \hline \text{Forecast} & 10 & 6 & 9 & 13 & 7 & 12 & 13 & 8 & 11 & 7 \\ \hline \end{array} \][/tex]
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