Question

The Carbondale Hospital is considering the purchase of a new ambulance. The decision will rest partly on the anticipated mileage to 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

Required:
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 = 0.5.

Answer 1

Answer: See explanation

Explanation:

a. The moving average is calculated as:

= sum demand for 2 yr/2

The moving average for next year will be:

= (3800+3700)/2

= 7500/2

= 3,750 Miles

(b) The mean absolute deviation(MAD)

= Sum(|Dt-Ft|)/n

Therefore, the moving average for Y3 will be:

= (3000+4000)/2

= 7000/2

= 3500

Moving Avge for Y4 F(4) will be:

= (4000+3400)/2

= 3700

Moving Avge for Y5 will be:

= (3400+3800)/2

= 7200/2

= 3600

Therefore, MAD will be:

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

(100+100+100)/3

= 300/3

= 100

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

So Weighted moving average for Y6 will be:

= ((3800 × 0.4)+(3700 × 0.6))/(0.4+0.6)

=1520 + 2220

= 3,740

MEAN ABSOLUTE DEVIATION:

= Sum(|Dt-Ft|)/n

Weighted moving average for Y3:

= (3000 × 0.4c+ 4000 × 0.6)/(0.4+0.6)

= 3600

Weighted moving average for Y4:

= (4000 × 0.4 + 3400 × 0.6)/(0.4+0.6)

= 3640

Weighted moving average for Y5:

= (3400 × 0.4+3800 × 0.6)/(0.4+0.6)

= 3640

Therefore, MAD

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

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

(d)Expomentioal Smoothing F(t) will now be:

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

Therefore, forecast will now be 3663 miles