*show work please! The Carbondale Hospital is considering the purchase of a new
ID: 388009 • Letter: #
Question
*show work please!
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
3100 3950 3450 3850 3750
a) Using a 2-year moving average, the forecast for year 6 =
3800
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 =
108.3
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
0.35
and
0.65
(the weight of
0.65
is for the most recent period) =
3785
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
0.35
and
0.65
=
155.8
miles (round your response to one decimal place). (Hint: You will have only 3 years of matched data.)
d) Using exponential smoothing with
alpha
=
0.40
and the forecast for year 1 being
3,100,
he forecast for year 6 =
3,664
miles (round your response to the nearest whole number).
Year
1 2 3 4 5
Mileage
3100 3950 3450 3850 3750
a) Using a 2-year moving average, the forecast for year 6 =
Explanation / Answer
Please refer below table for relevant data :
Year
Mileage
Forecast ( 2 yr moving average)
Absolute Deviation
Forecast ( 2 yr weighted moving average)
Absolute deviation
Forecast ( exponential smoothing)
1
3100
3100
2
3950
3100
3
3450
3525
75
3652.5
202.5
3440
4
3850
3700
150
3625
225
3444
5
3750
3650
100
3710
40
3606
6
3800
3785
3664
Sum =
325
467.5
Following to be noted :
a)Forecast basis 2 year moving average :
Ft = ( At-1 + At-2 ) / 2
Where,
Ft = Forecast for period t
At-1, At-2 = Actual mileage for period t-1 and t-2 respectively
Using 2 year moving average , forecast for year 6 = 3800
b)Absolute deviation for period t = absolute difference between Forecast and corresponding actual mileage for period t
Sum of absolute Deviation values = 325
Mean absolute deviation ( MAD ) = 325 / 3 ( i.e. number of observations ) = 108.33
If a 2 year moving average is used to make a forecast , the MAD based on this = 108.3 ( rounded to 1 decimal place)
c)Using 2 year weighted moving average with weights 0.35 and 0.65 ( with weight 0.65for the most recent period ) :
Ft = 0.65 x At-1 + 0.35 x At-2
Ft = Forecast for period t
At-1, At-2 = Actual mileage for period t-1 and t-2 respectively
The forecast for year 6 using weighted moving average = 3785
Sum of absolute deviation values = 467.5
Mean Absolute deviation ( MAD ) = 467.5/ 3 = 155.83
The MAD for forecast developed using a 2 year weighted moving average with weights 0.65 and 0.35 = 155.8 (rounded to 1 decimal place)
Ft = alpha x At-1 + ( 1 – alpha)x Ft-1
= 0.40 x At-1 + 0.60 x Ft-1
Where,
Ft, Ft-1 = Forecasts for period t and t-1 respectively
At-1 = Actual mileage for period t-1
Alpha = exponential smoothing constant = 0.4
Basis above, forecast for period 6 = 3664
Forecast for year 6 using exponential smoothing forecast = 3664
Year
Mileage
Forecast ( 2 yr moving average)
Absolute Deviation
Forecast ( 2 yr weighted moving average)
Absolute deviation
Forecast ( exponential smoothing)
1
3100
3100
2
3950
3100
3
3450
3525
75
3652.5
202.5
3440
4
3850
3700
150
3625
225
3444
5
3750
3650
100
3710
40
3606
6
3800
3785
3664
Sum =
325
467.5
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