Question

The Cleveland Patient Transfer Company is considering the purchase of a new ambulance. The decision will rest partly on the anticipated distance to be driven next year. The kilometres driven during the past five years are as follows:

Year	Distance (Km)
1	3000
2	4000
3	3400
4	3800
5	3700

1. Forecast the number of kilometres for next year using a two-year moving average.

2. Find the MAD based on the two-year moving average forecast in part (a).

(Hint: You will have only three years of matched data.)

3. Use a weighted two-year moving average with weights of 0.4 and 0.6 to forecast next year’s mileage. (The weight of 0.6 is for the most recent year.)

4. What MAD results from using this approach to forecasting? (Hint: You will have only three years of matched data.)

Answer 1

The two year moving average method takes the average of previous 2 years to calculate current years forecast. For example for year 3, forecast is (3000 + 4000) / 2 = 3500 Km

The MAD (Mean absolute deviation) is the mean of the absolute difference between the actual value and forecasted value. For example for year 3, in case of two year moving average, deviation is |3400 - 3500| = 100. MAD is calculated by taking average of years 3,4 and 5.

For weighted average forecast, we apply the weights applicable for a given year and calculate the weighted average. For example for year 3, forecast is 4000x0.6 + 3000x0.4 = 3600

a) Using the above, we calculate the two-year moving average and the MAD.

Year	Distance (km)	Forecast	Deviation
1	3000
2	4000
3	3400	3500	100
4	3800	3700	100
5	3700	3600	100

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

b) Using weighted two-year moving average we get,

Year	Distance (km)	Forecast	Deviation
1	3000
2	4000
3	3400	3600	200
4	3800	3640	160
5	3700	3640	60

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