The Carbondale Hospital is considering the purchase of ambulance. The TheXarbond

Question

The Carbondale Hospital is considering the purchase of ambulance. The TheXarbondale Hospital is considering the purchase of ambulance. The decision will rest partly on the anticipated mileage" be driven next year. The miles driven during the past 5
years are as follows:

Year

Mileage

1

3000

2

4000

3

3400

4

3800

5

3700

a) Forecast the mileage for next year using a 2-year moving average.
b) Find the MAD based on the 2-year moving average forecast in part (a), (Hint: You will have only 3 years of matched data.)
c) Use a weighted 2-year moving average with weights of .4 and .6 to forecast next year's mileage. (The weight of .6 is for the most recent year.) What MAD results from using this approach to forecasting? (Hint: You will have only 3 years of matched data.)
d) Compute the forecast for year 6 using exponential smoothing, an initial forecast for year 1 of 3,000 miles, and a = .5.

*****PLEASE SHOW WORK

Year

Mileage

1

3000

2

4000

3

3400

4

3800

5

3700

Explanation / Answer

(a) Moving average = sum demand in 2 yr period/2

Moving average for Nxt yr = (3800+3700)/2 = 3,750 Miles

(b) MEAN ABSOLUTE DEVIATION (MAD) = Sum(|Dt-Ft|)/n

where Dt is demand in Period t & Ft is FOrecats in period t

So Mving Avge for Y3 ie F(3) = (3000+4000)/2 = 3500

& D3 = 3400

So Mving Avge for Y4 ie F(4) = (4000+3400)/2 = 3700

& D4 = 3800

So Mving Avge for Y5 ie F(5) = (3400+3800)/2 = 3600

& D5 = 3700

So MAD = Sum(|3500-3400|+|3700-3800|+|3600-3700|)/3

ie MAD = (100+100+100)/3 = 100

(c) Weighted moving average = sum (weight in period n)*(demand in period n)/Sum weights

So Weighted moving average Y6 =

((3800*0.4)+(3700*0.6))/(0.4+0.6)

= 3,740

MEAN ABSOLUTE DEVIATION (MAD) = Sum(|Dt-Ft|)/n

where Dt is demand in Period t & Ft is FOrecats in period t

So Wtd Mving Avge for Y3 ie F(3)

= (3000*0.4+4000*0.6)/(0.4+0.6) = 3600

& D3 = 3400

So Wtd Mving Avge for Y4 ie F(4)

= (4000*0.4+3400*0.6)/(0.4+0.6) = 3640

& D4 = 3800

So Wtd Mving Avge for Y5 ie F(5)

= (3400*0.4+3800*0.6)/(0.4+0.6) = 3640

& D5 = 3700

So MAD = Sum(|3600-3400|+|3640-3800|+|3640-3700|)/3

ie MAD = (200+160+60)/3 = 140

(d)Expomentioal Smoothing F(t)

F(t) =F(t-1)+a*(A(t-1) -F(t-1))

SO F(1) = 3000 + 0.5*(3000-3000) = 3000

F(2) = 3000 + 0.5*(4000-3000) = 3500

F(3) = 3500 + 0.5*(3400-3500) = 3450

F(4) = 3450 + 0.5*(3800-3450) = 3625

F(5) = 3625 + 0.5*(3700-3625) = 3663

So FOrecast is 3663 miles

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