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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.

Respuesta :

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

A. The moving average is 3,750 Miles

B. The mean absolute deviation(MAD) 100

C. Weighted moving average 3,740

D. Exponential Smoothing F(t) 3663 Miles

Calculation of Weighted average

a. When The moving average is calculated as:

Then = sum demand for 2 yr/2

After that The moving average for next year will be:

Then = (3800+3700)/2

Now, = 7500/2

= 3,750 Miles

(b) When The mean absolute deviation(MAD)

Then = Sum(|Dt-Ft|)/n

Therefore, When the moving average for Y3 will be:

Then = (3000+4000)/2

After that = 7000/2

= 3500

Then the Moving average for Y4 F(4) will be:

After that = (4000+3400)/2

Then = 3700

Now Moving average for Y5 will be:

After that = (3400+3800)/2

Then = 7200/2

= 3600

Now MAD will be:

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

(100+100+100)/3

After that = 300/3

= 100

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

So The Weighted moving average for Y6 will be:

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

After that =1520 + 2220

Then = 3,740

The MEAN ABSOLUTE DEVIATION:

Then = Sum(|Dt-Ft|)/n

When the Weighted moving average for Y3:

After that = (3000 × 0.4c+ 4000 × 0.6)/(0.4+0.6)

= 3600

Weighted moving average for Y4:

Then = (4000 × 0.4 + 3400 × 0.6)/(0.4+0.6)

= 3640

Then Weighted moving average for Y5:

= (3400 × 0.4+3800 × 0.6)/(0.4+0.6

= 3640

Thus, MAD

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

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

(d) The Exponential Smoothing F(t) will now be:

SO F(1) = 3000 + 0.5 × (3000-3000)

Then = 3000

F(2) = 3000 + 0.5 × (4000-3000)

Then = 3500

F(3) = 3500 + 0.5 × (3400-3500)

After that = 3450

F(4) = 3450 + 0.5 × (3800-3450)

Then = 3625

F(5) = 3625 + 0.5 × (3700-3625)

Now, = 3663

Thus, forecast will now be 3663 miles

Find more information about Weighted average here:

https://brainly.com/question/26595359

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