Bass Pro Shops $($BPS$)$ needs assistance forecasting the demand for a popular family of boats. In the table below, managers have provided the actual demand data for the last $5$ months.

Rounding instructions:

Carry all calculations to at least three decimal places.

Enter all forecasts rounded to the nearest tenth $($one decimal place$).$

Enter MAPE as a percentage rounded to the nearest hundredth of a percent $($e$.$g$.0\mathrm{.}11746$ should be entered as $11\mathrm{.}75\%).$

a$.$ In the past BPS has relied on two qualitative approaches for its forecasting: $1)$ Sales force survey; and $2)$ Executive opinion. Over the past $5$ months, the MAPE for the executive opinion forecast has been $21\%.$ The Sales Force Forecast is provided below. Compute the MAPE for this forecast and determine which of the two forecasts has performed better over the past $5$ months.

Month

Actual Demand

Sales Force Forecast

$1$

$605$

$785$

$2$

$610$

$501$

$3$

$749$

$928$

$4$

$847$

$616$

$5$

$923$

$1120$

MAPE for Forecast based on Sales Force Projections: $\%$

Which forecast performs better according to the MAPE? $($Award any ties to the Sales Force$).$

b$.$ Going forward BPS would like to rely on a more quantitative approach using time series methods. Compute an exponential smoothing forecast for Month $6$ with $\backslash$alpha $=0\mathrm{.}2.$

Start with the naive forecast for Period $2.$

F$6=$ units.

c$.$ Compute a weighted moving average $($WMA$)$ forecast for Month $6$ with weights of wt$-1=0\mathrm{.}3$ and wt $=0\mathrm{.}7.$

F$6=$ units.

d$.$ Incorporate trend into your forecast by applying a double exponential smoothing approach starting with your forecast for Period $5.$ Use parameter values of $\backslash$alpha $=0\mathrm{.}2,\backslash$beta $=0\mathrm{.}5$ and start with initial estimates for Period $4$ of S$4=650$ and T$4=50.$ Complete the table to enter the correct double exponential smoothing forecast.

Period

Actual Demand

St

Tt

Dbl$.$ Exp. Smoothing Forecast

$\backslash$alpha $=0\mathrm{.}2,\backslash$beta $=0\mathrm{.}5$

$4$

$847$

$650$

$50$

$5$

$923$

$6$