Sam Houston is considering the purchase of new utility vehicles. The decision wi

Question

Sam Houston is considering the purchase of new utility vehicles. The decision will rest partly on the anticipated mileage to be driven by each vehicle next year. The miles driven during the past five years are as follows:

Year

Mileage

1

4,500

2

5,000

3

5,500

4

5,800

5

5,700

6

5,300

7

5,900

                       

1. Forecast the mileage for the 8th year using a 2-year moving average

2. Find the MAD and MAPE based on the 2 year moving average (Hint: You will have only 5 years of matched data).

3. Compute the forecast for years 2 through 8 using exponential smoothing, an initial forecast for year one of 4000 miles, and alpha = .1 and alpha of .5    Which alpha predicts the best forecast?

Year

Mileage

1

4,500

2

5,000

3

5,500

4

5,800

5

5,700

6

5,300

7

5,900

Chaptar 4 Problem 1 (YOU MUST SHOW ALL OF YOUR WORK)

Explanation / Answer

1.

2 year MA forecast for year 8 = (5300+5900)/2 = 5600

2.

MAD = Sum of absolute errors / no. of observations = (750+550+50+450+400)/5 = 440

MAPE = Mean of the absolute percentage error = (13.64+9.48+.88+8.49+6.78)/5 = 7.85

3.

MAD when alpha of .1 = (500+950+1355+1519.5+1267.55+740.8+1266.72)/7 = 1085.65

MAD when alpha of .5 = (500+750+875+737.5+268.75+265.63+467.19)/7 = 552.01

Alpha of .5, predicts better forecast, because it has lower value of MAD.

Year Mileage 2 Year MA Difference between actual and forecast Absolute Difference Absolute % error (%) 1 4,500 2 5,000 3 5,500 4750 750 750 13.64 4 5,800 5250 550 550 9.48 5 5,700 5650 50 50 0.88 6 5,300 5750 -450 450 8.49 7 5,900 5500 400 400 6.78 8 5600

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