Consider the data above:

a$)$ Use a weighted moving average to forecast next year's January sales. Use the weights $(3/6),(2/6)$ and $(1/6),$ giving more weight to the most recent data.

b$)$ Use exponential smoothing with $\backslash$alpha $=0\mathrm{.}6,0\mathrm{.}4,0\mathrm{.}2$ to forecast the next year's February sale. Suppose the initial forecast for January was $$22$ million.

$3.$ The number of heart surgeries performed at the General Hospital has increased steadily in recent years. Hospital administration is looking for the best method to forecast demand for those surgeries in year six. Data for the last fifteen years is shown in the table.

Year $/$ Demand

$1145$

$2150$

$3162$

$4156$

$5158$

$6182$

$7166$

$8160$

$9145$

$10180$

$11195$

$12200$

$13190$

$14163$

$15192$

The hospital administration is considering the following forecasting methods. Begin the error measurement in year three to compare all methods in the same years.

a$)$ Indicate the MAD, MEC, MAPE for a naive demand forecast.

b$)$ Exponential smoothing with $\backslash$alpha $=0\mathrm{.}6.$ The initial forecast for year one is $145,$ the same as actual demand.

c$)$ Exponential smoothing with $\backslash$alpha $=0\mathrm{.}9.$ The initial forecast for year one is $145,$ the same as actual demand.

d$)$ Two$-$year moving average.

e$)$ Weighted moving average, with weights of e$0\mathrm{.}6$ and $0\mathrm{.}4,$ giving more weight to the most recent data.