Problem #$1$: $(30$ points$)$

$-4\mathrm{.}10$ Data collected on the yearly registrations for a Six

Sigma seminar at the Quality College are shown in the following

table:

a$)$ Develop a $3-$year moving average to forecast registrations for each of the

years where possible, including year $12.$

b$)$ Estimate demand again for the same years as in a$)$ with a $3-$year weighted

moving average in which registrations in the most recent year are given a

weight of $2,$ and registrations in the other $2$ years are each given a weight

of $1.$

c$)$ Use exponential smoothing with a smoothing constant of $0\mathrm{.}3$ to forecast

the registrations at the seminar in year $12.$ To begin the procedure,

assume that the forecast for year $1$ was $5,000$ people signing up

d$)$ What are the MAD and the MSE for the forecast in part a$),$ b$)$ and c$)?$

e$)$ Based on the MSE, which of the forecasting methods is the better one for

this data set? You are expected to help yourself with either HLOOKUP or

VLOOKUP so that your Excel Model tells you which forecasting method is

the better one based on MSE.

Problem #$2$: $(25$ points$)$

$-\mathrm{.}4\mathrm{.}31$ Emergency calls to the $911$ system of Durham,

North Carolina, for the past $24$ weeks are shown in the following

table:

f$)$ Select any $3$ alpha values for an exponential smoothing forecast, and

determine which alpha is the better one using the MAPE to measure the

forecasting error.

g$)$ Using the alpha found in part a$),$ find the forecast for week $25$ using

exponential smoothing.

h$)$ Using the alpha in a$)$ and $=0\mathrm{.}2,$ and assuming that the initial forecast was

$50$ calls, and the initial trend is $1,$ find the forecast for week $25$ using a

trend$-$adjusted exponential smoothing model.

i$)$ Using MAPE to measure the forecast error, determine which of the two

methods $(b$ and $c)$ is a better method for this data. You are expected to use

one of the LOOKUP functions.