Heidi favors using a two period moving average but Tim is "an exponential-smoothing man." Tim's demand forecast for May was identical to Heidi's. What value of alpha would Tim need to use in order for his June forecast to be identical to Heidi's if each sticks with their preferred technique? Note that Tim's forecast for May was identical to Heidi's two-period moving average for May. $$\begin{array} { | c | c | }
\hline \text { Month } & \text { Demand } \
\hline \text { January } & 154 \
\hline \text { February } & 148 \
\hline \text { March } & 214 \
\hline \text { April } & 180 \
\hline \text { May } & 225 \
\hline \text { June } & 246 \
\hline
\end{array}$$
A).085
B).196
C).237
D).348

Question

Heidi favors using a two period moving average but Tim is "an exponential-smoothing man." Tim's demand forecast for May was identical to Heidi's. What value of alpha would Tim need to use in order for his June forecast to be identical to Heidi's if each sticks with their preferred technique? Note that Tim's forecast for May was identical to Heidi's two-period moving average for May. $$\begin{array} { | c | c | } 
\hline \text { Month } & \text { Demand } \
\hline \text { January } & 154 \
\hline \text { February } & 148 \
\hline \text { March } & 214 \
\hline \text { April } & 180 \
\hline \text { May } & 225 \
\hline \text { June } & 246 \
\hline
\end{array}$$
A).085
B).196
C).237
D).348

Quizplus · Accepted Answer

For Tim's June forecast to match Heidi's, using exponential smoothing, the alpha ($\alpha$) value must be such that the forecast incorporates the most recent demand (May's demand) exactly as a two-period moving average would. A two-period moving average for June would average April and May's demands: $\frac{180 + 225}{2} = 202.5$. Since May's forecast was identical for both, and assuming Tim's forecast for June also needs to be 202.5 to match Heidi's two-period moving average, we can set up the exponential smoothing formula for June's forecast based on May's actual demand and forecast. The formula for exponential smoothing is $F_{t+1} = \alpha D_t + (1-\alpha)F_t$, where $F_{t+1}$ is the forecast for the next period, $D_t$ is the actual demand in the current period, and $F_t$ is the forecast for the current period. Given that $F_{t+1} = 202.5$, $D_t = 225$, and $F_t = 202.5$ (since Tim's forecast for May was identical to Heidi's and thus also his starting point for June), we can solve for $\alpha$:$$202.5 = \alpha \cdot 225 + (1-\alpha) \cdot 202.5$$Solving for $\alpha$ gives $\alpha = 0.196$, which means Tim would need to use an alpha value of 0.196 for his June forecast to match Heidi's two-period moving average forecast.

Heidi Favors Using a Two Period Moving Average but Tim