Practise Question $\frac{?}{?}$&$33$ Megrawhill Page $99$

Blue Bell Inc $($BBI$)$ is a company that collects smartwatches. Reprocesses them and resells them to consumers. Historical monthly quantities collected smartwatches $("$returns$")$ in the last seven months are displayed in the table below.

$\backslash$table$[[$Month$,$August,September,October,November,December,January,February$],[\backslash$table$[[$Units$],[$Returned$]],59,86,92,90,76,64,88]]$

a$)$ Given the above data, calculate the forecast using a weighted moving average to forecast for the $8^{th}$ month, i$.$e$.$ March. Weights of $0\mathrm{.}18,0\mathrm{.}34,$ and $0\mathrm{.}48$ for December, January, and February, respectively.

b$)$ Calculate the sales forecast for March $(88^{th}$ month$)$ using simple exponential smoothing with $=0\mathrm{.}30$ when the forecast for January is $74$ units.

c$)$ Calculate the exponential smoothing with trend forecast of March $(8^{th}$ month$)$ for the above data using an $($Alpha$)$ of $0\mathrm{.}40,$ a $($delta$)$ of $0\mathrm{.}70,$ a January forecast $[$FJanuary$]$ of $93$ units and an estimated January trend $[$TJanuary$]$ of $5\mathrm{.}65,$ respectively.

d$)$ Based on a particular forecasting mothod, the BBI team forecasted the return of smartwatch for each month. Forecasted and the actual return of smartwatches for each month's data are summarized in the table below. Develop a tracking signal $($TS$)$ and state whether it stays within the acceptable limits$,$ which BBI defines as $+-3\mathrm{.}75$ MADs. You must show your work by filling out the table $[$Copy the table$].$ Is this a good or poor forecasting model? Briefly state your reason. $[$A simple YES or NO answer receives ZERO mark.$]$

$\backslash$table$[[$Month$,\backslash$table$[[$Actual$],[$Returns$]],\backslash$table$[[$Forecast$],[$Returns$]],\backslash$table$[[$Forecast$],[$Error$]],($RSFE$),\backslash$table$[[$Absolute$],[$Deviation$]],\backslash$table$[[$Sum of$],[$Absolute$],[$Deviation$]],$MAD,TS$],[$August$,59,54,,,,,,],[$September$,86,99,,,,,,],[$October$,92,62,,,,,,],[$November$,90,85,,,,,,],[$December$,76,86,,,,,,],[$January$,64,94,,,,,,],[$February$,88,90,,,,,,]]$