Weighted moving average $($WMA$)$ method is basically the same as moving averages, with one

major exception. With weighted moving averages, the weight assigned to each past data point used

in the calculation can vary. In this way, more influence can be given to some data points,

typically the most recent demand point. The formulation is given below:

n is the number of periods being used.

Now, solve the following question:

A demand pattern for $10$ periods for a product was given as $127,113,121123,117,109,131,115,$

$127$ and $118.$ Forecast for the demand for period $11$ using each of the following methods: a

$3-$month weighted moving average using weights of $0\mathrm{.}2,0\mathrm{.}3$ and $0\mathrm{.}5$; and exponential smoothing

with a smoothing constant of $0.$XX $($last two digits of your student ID after the decimal point $($for

example: if your student ID is $63171234,$ you should use $\backslash$alpha $=0\mathrm{.}34)$

Compute the MAD for each method to determine which method would be preferable under the

circumstances. Complete the necessary cells of the following table:

Period Demand $3-$month WMA Exponential Smoothing

$($note that F$2=$D$1=127)$

$1$

$2$

$3$

$4$

$5$

$6$

$7$

$8$

$9$

$10$

$11$

MAD