Ch $3$: Forecasting: Tracking Signals, Mad, Exponential Smoothing, Control Charts Media Consultants $(10$ Pts$).$

Media Consultants uses proven techniques to measure forecast accuracy and to determine when the forecast needs to be reviewed$/$updated$.$

The following data has been extracted from their information system:

$\backslash$begin$\{$tabular$\}\{|$l$|$l$|$l$|$l$|$l$|$l$|\}$

$\backslash$hline Month & $\backslash$begin$\{$tabular$\}\{$l$\}$

Actual Sales $\backslash \backslash$

$(\backslash$$million$)$

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$l$\}$

Forecast $\backslash \backslash$

$(\backslash$$million$)$

$\backslash$end$\{$tabular$\}$ & & & $\backslash \backslash$

$\backslash$hline $1$ & $22$ & $30$ & & & $\backslash \backslash$

$\backslash$hline $2$ & $22$ & $24$ & & & $\backslash \backslash$

$\backslash$hline $3$ & $22$ & $18$ & & & $\backslash \backslash$

$\backslash$hline $4$ & $22$ & $15$ & & & $\backslash \backslash$

$\backslash$hline $5$ & $24$ & $15$ & & & $\backslash \backslash$

$\backslash$hline $6$ & $24$ & $19$ & & & $\backslash \backslash$

$\backslash$hline $7$ & $24$ & $24$ & & & $\backslash \backslash$

$\backslash$hline $8$ & $23$ & $26$ & & & $\backslash \backslash$

$\backslash$hline $9$ & $23$ & $32$ & & & $\backslash \backslash$

$\backslash$hline $10$ & $23$ & $27$ & & & $\backslash \backslash$

$\backslash$hline $11$ & $23$ & $22$ & & & $\backslash \backslash$

$\backslash$hline $12$ & $22$ & $16$ & & & $\backslash \backslash$

$\backslash$hline $13$ & $22$ & $14$ & & & $\backslash \backslash$

$\backslash$hline $14$ & $22$ & $18$ & & & $\backslash \backslash$

$\backslash$hline $15$ & $22$ & $21$ & & & $\backslash \backslash$

$\backslash$hline $16$ & $21$ & $23$ & & & $\backslash \backslash$

$\backslash$hline $17$ & $21$ & $25$ & & & $\backslash \backslash$

$\backslash$hline $18$ & $20$ & $28$ & & & $\backslash \backslash$

$\backslash$hline $19$ & $20$ & & & & $\backslash \backslash$

$\backslash$hline $20$ & $20$ & & & & $\backslash \backslash$

$\backslash$hline & & & & & $\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

a$).$ Compute a tracking signal for months $11$ through $20.$ Compute an initial value of MAD for month $11,$ and then update it for each month using exponential smoothing with alpha $-\mathrm{.}1.$ What can you conclude? Assume limits of $\backslash (+/-4\backslash ).$

b$).$ Using the first half of the data construct a control chart with $2$ s limits$.$ What can you conclude?

c$).$ Plot the last $10$ errors on the control chart. Are the errors random? What is the implication of this?

Ch $3\_$Forecasting$\_$Tracking Signals$\_$Mad$\_$Exponential Smoothing$\_$Control Charts