A company keeps track of unit sales and notes a strong trend during the past eight periods. They use an adjusted exponential smoothing model with an alpha equal to 0.7 and a beta equal to 0.6. Using the demand data and previous forecasts shown in the table, develop a forecast for period 4. $$\begin{array} { | c | c | c | c | c | }
\hline \text { Week } & \text { \# Units } & \begin{array} { c }
\text { Unadjusted } \
\text { Forecast }
\end{array} & \text { Trend } & \begin{array} { c }
\text { Adjusted } \
\text { Forecast }
\end{array} \
\hline 1 & 68 & 65.0 & 0.0 & 65.0 \
\hline 2 & 72 & 67.1 & 1.3 & 68.4 \
\hline 3 & 80 & & & \
\hline 4 & 93 & & & \
\hline 5 & 108 & & & \
\hline 6 & 121 & & & \
\hline 7 & 125 & & & \
\hline 8 & 139 & & & \
\hline
\end{array}$$
A)82.2
B)84.9
C)87.5
D)91.6

Question

A company keeps track of unit sales and notes a strong trend during the past eight periods. They use an adjusted exponential smoothing model with an alpha equal to 0.7 and a beta equal to 0.6. Using the demand data and previous forecasts shown in the table, develop a forecast for period 4. $$\begin{array} { | c | c | c | c | c | } 
\hline \text { Week } & \text { \# Units } & \begin{array} { c } 
\text { Unadjusted } \
\text { Forecast }
\end{array} & \text { Trend } & \begin{array} { c } 
\text { Adjusted } \
\text { Forecast }
\end{array} \
\hline 1 & 68 & 65.0 & 0.0 & 65.0 \
\hline 2 & 72 & 67.1 & 1.3 & 68.4 \
\hline 3 & 80 & & & \
\hline 4 & 93 & & & \
\hline 5 & 108 & & & \
\hline 6 & 121 & & & \
\hline 7 & 125 & & & \
\hline 8 & 139 & & & \
\hline
\end{array}$$
A)82.2
B)84.9
C)87.5
D)91.6

Quizplus · Accepted Answer

To calculate the adjusted forecast for period 4, we need to use the following formulas:

$	ext{Forecast}_{t}=\alpha(	ext{Demand}_{t-1}-	ext{Trend}_{t-1})+(1-\alpha)(	ext{Forecast}_{t-1}+	ext{Trend}_{t-1})$

$	ext{Trend}_{t}=\beta(	ext{Forecast}_{t}-	ext{Forecast}_{t-1})+(1-\beta)	ext{Trend}_{t-1}$

We are given that $\alpha=0.7$ and $\beta=0.6$. We already have the unadjusted forecast and trend values for periods 1 and 2. Using these values, we can calculate the adjusted forecast and trend values for periods 3 and 4:

$	ext{Forecast}_{3}=0.7(72-1.3)+(1-0.7)(68.4+1.3)=72.98$

$	ext{Trend}_{3}=0.6(72.98-68.4)+(1-0.6)1.3=1.792$

$	ext{Forecast}_{4}=0.7(80-1.792)+(1-0.7)(72.98+1.792)=82.203$

Therefore, the best choice is A) 82.2.

A Company Keeps Track of Unit Sales and Notes a Strong