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	3,050	4,050	3,450	3,750	3,750

^{a)Using a 2-year moving average, the forecast for year 6 (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 (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 0.40 and 0.60 (the weight of 0.60 is for the most recent period) = 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 0.40 and 0.60 (round your response to one decimal place). (Hint: You will have only 3 years of matched data.)?}

^{d) Using exponential smoothing with alpha ? 0.30 and the forecast for year 1 being 3,050, the forecast for year 6 (round your response to the nearest whole number).?}

Answer 1

A) Simple moving averages:

The simplest model for extrapolative forecasting is the method of simple moving averages. The model has a single parameter, that is, the number of periods to be considered for computing the moving average.

We have to calculate 2 year Moving Average for period 6.

Formula: Forecast of (N)^th = Average (Mileage of (N-1)^th, Mileage of (N-2)^th)

Year	Mileage	Forecast
1	3050
2	4050
3	3450	=Average(3050,4050)=(3050+4050)=3550
4	3750	=Average(4050,3450)=(4050+3450)=3750
5	3750	=Average(3450,3750)=(3450+3750)=3600
6		=Average(3750,3750)=(3750+3750)=3750

So, Forecast of period 6 = 3750

B) Mean Absolute Deviation =

Year(N)	Mileage	Forecast by Simple Moving Average	Forecast Error =Mileage-Forecast	Absolute Deviation	Cumulative Absolute Deviation(CAD)	Mean Absolute Deviation =CAD/N
1	3050
2	4050
3	3450	3550	=3450-3550=-100	100	100	=100/3=33.3
4	3750	3750	=3750-3750=0	0	100	=100/4=25
5	3750	3600	=3750-3600=150	150	250	=250/5=50
6		3750

C) Here W_t-1=0.6 ,W_t-2=0.4

Forecast F_t = M_t-1 * W_t-1 + M_t-2 * W_t-2

Year	Mileage(M)	Forecast by Weighted Moving Average(Ft)	Forecast Error	Absolute Deviation	Cumulative Absolute Deviation(CAD)	Mean Absolute Deviation =CAD/N
1	3050
2	4050
3	3450	=4050*0.6+3050*0.4 = 3650	200	200	200	66.7
4	3750	=3450*0.6+4050*0.4 = 3690	-60	60	260	65.0
5	3750	=3750*0.6+3450*0.4 = 3630	-120	120	380	76.0
6		=3750*0.6+3750*0.4 = 3750

D)

Year	Mileage(Mn)	M*	Fn-1 * (1-)
1	3050		2135	=M1=3050
2	4050	915
3	3450	1215
4	3750	1035
5	3750	1125
6		1125