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   1   2   3   4   5
Mileage   3,000   3,950   3,450   3,800   3,750

​a) Using a​ 2-year moving​ average, the forecast for year 6​ =

3775 miles ​(round your response to the nearest whole​ number).

​b) If a​ 2-year moving average is used to make the​ forecast, the MAD based on this​ = 83.3 miles ​(round your response to one decimal​ place). ​ (Hint: You will have only 3 years of matched​ data.)

​c) The forecast for year 6 using a weighted​ 2-year moving average with weights of 0.45 and 0.55 ​(the weight of 0.55 is for the most recent​ period) = 3773 miles ​(round your response to the nearest whole​ number).

The MAD for the forecast developed using a weighted​ 2-year moving average with weights of 0.45 and 0.55 = 102 miles ​(round your response to one decimal​ place).  ​(Hint: You will have only 3 years of matched​ data.)

​d) Using exponential smoothing with alpha α​ = 0.40 and the forecast for year 1 being 3,000​, the forecast for year 6​ =________________ miles ​(round your response to the nearest whole​ number).

Answer 1

Please refer filled up data as below as per requirement .

Forecast basis 2 year moving average : Ft = ( At-1 +At-2)/2

Forecast basis 2 year weighted moving average = Ft = 0.55 x At-1 + 0.45xAt-2

The applicable formula for exponential smoothing is :

Ft = alpha x At-1 + ( 1- alpha) x Ft-1

Ft = Forecast for period t

Ft-1 = Forecast for period t-1

At-1 = Actual for period t-1

Alpha = smoothing constant = 0.40

Absolute deviation = Absolute difference between actual value vs forecasted value

MAD ( Mean absolute deviation) = sum of absolute deviation/ number of observations

Year	Actual data	Forecast-2 year moving average	absolute deviation	Forecast - 2 year weighted moving average	Absolute deviation	Forecast - exponential smoothing
1	3000					3000
2	3950					3000
3	3450	3475	25	3522.5	72.50	3380
4	3800	3700	100	3675	125.00	3408
5	3750	3625	125	3643	107.50	3565
6		3775		3773		3639
		Sum =	250		305.00
		MAD =	83.3		101.7

MAD for 2 year moving average = 83.3

MAD for weighted 2 year moving average =01.7

Forecast for period 6 basis:

2 year moving average = 3775

2 year weighted moving average = 3773

Exponential smoothing = 3639