Professor Z needs to allocate time among several tasks next week to include time for students' appointments. Thus, he needs to forecast the number of students who will seek appointments. He has gathered the following data:
$$\begin{array} { | c | c | }
\hline \text { Week } & { \text { \# of students } } \
\hline 6 \text { weeks ago } & 85 \
\hline 5 \text { weeks ago } & 110 \
\hline 4 \text { weeks ago } & 95 \
\hline 3 \text { weeks ago } & 80 \
\hline 2 \text { weeks ago } & 65 \
\hline \text { Last week } & 50 \
\hline
\end{array}$$
What is the forecast for this week using exponential smoothing with trend if ? = 0.5 and ? = 0.1? Assume the forecast for last week was 65 and the forecast for two weeks ago was 75, and that the trend estimate for last week's forecast was ?5.
A) 49
B) 50
C) 52
D) 65
E) 78

Question

Professor Z needs to allocate time among several tasks next week to include time for students' appointments. Thus, he needs to forecast the number of students who will seek appointments. He has gathered the following data:
$$\begin{array} { | c | c | } 
\hline \text { Week } & { \text { \# of students } } \
\hline 6 \text { weeks ago } & 85 \
\hline 5 \text { weeks ago } & 110 \
\hline 4 \text { weeks ago } & 95 \
\hline 3 \text { weeks ago } & 80 \
\hline 2 \text { weeks ago } & 65 \
\hline \text { Last week } & 50 \
\hline
\end{array}$$
What is the forecast for this week using exponential smoothing with trend if ? = 0.5 and ? = 0.1? Assume the forecast for last week was 65 and the forecast for two weeks ago was 75, and that the trend estimate for last week's forecast was ?5.
A) 49
B) 50
C) 52
D) 65
E) 78

Quizplus · Accepted Answer

Exponential smoothing with trend involves updating the forecast using the formula $F_t = F_{t-1} + T_{t-1} + \alpha(D_{t-1} - F_{t-1}) + \beta(T_{t-1} - T_{t-2})$, where $F_t$ is the forecast for the current period, $F_{t-1}$ is the forecast for the previous period, $T_{t-1}$ is the trend estimate for the previous period, $D_{t-1}$ is the actual demand in the previous period, and $\alpha$ and $\beta$ are smoothing constants for the level and trend, respectively. Given $F_{last week} = 65$, $T_{last week} = -5$, $D_{last week} = 50$, $F_{two weeks ago} = 75$, and $T_{two weeks ago} = F_{last week} - F_{two weeks ago} = 65 - 75 = -10$, the forecast for this week is calculated as follows:$$F_{this week} = 65 - 5 + 0.5(50 - 65) + 0.1(-5 - (-10))$$$$F_{this week} = 60 - 7.5 - 0.5$$$$F_{this week} = 52$$Therefore, the forecast for this week using exponential smoothing with trend is 52.

Professor Z Needs to Allocate Time Among Several Tasks Next