The number of heart surgeries performed at Heartville General Hospital has incre
ID: 363250 • Letter: T
Question
The number of heart surgeries performed at Heartville General Hospital has increased steadily over the past several years. The hospital's administration is seeking the best method to forecast the demand for such surgeries in year 6. The data for the past five years are shown below. 4 56 59 The hospital's administration is considering the following forecasting methods. Begin error measurement in year 3, so all methods are compared for the same years. i. Exponential smoothing, with -06. Let the initial forecast for year 1 be 42, the same as the actual demand. 11. Exponential smoothing, with = 0.9. Let the initial forecast for year 1 be 42, the same as the actual demand. iii. Trend projection with regression. iv. Two-year moving average. v. Two-year weighted moving average, using weights 0.6 and 0.4, with the more recent data given more weight. If MAD is the performance criterion chosen by the administration, which forecasting method should it choose?Explanation / Answer
Formula for exponential smoothing :
Please note formulation of equations under different forecasting methods :
a)Ft = alpha x Dt-1 + ( 1 – alpha) x Ft-1 alpha = exponential smoothing factor= 0.6 , Dt-1= Demand for period t-1, Ft,Ft-1= Forecast for period t and t-1
Or, Ft = 0.6xDt-1 + 0.4 x Ft-1
b) Ft = alpha x Dt-1 + ( 1 – alpha) x Ft-1 alpha = exponential smoothing factor= 0.9 , Dt-1= Demand for period t-1, Ft,Ft-1= Forecast for period t and t-1
Or, Ft = 0.9xDt-1 + 0.1 x Ft-1
2)Trend projection with regression equation :
Let the formula be :
Y = a + b.X a, b = constants , X ( Independent variable ) = Year,
Y( Dependent variable) = Forecasted demand
By placing values Year and Demand in two separate columns in excel and applying the function LINEST ( ) , we obtain following values of a and b :
‘a = 38.1 b = 4.3
Therefore , Y = 38.1 + 4.3.X
3) Equation basis 2 year moving average :
Ft = ( Dt-1 + Dt-2 ) / 2
Ft = Forecast for period t
Dt-1 = Demand for period t-1
Dt-2 = demand for period t-2
4) Equation basis 2 year weighted moving average of 0.6 and 0.4, with most recent data having 0.6 weightage
Ft = 0.6 x Dt-1 + 0.4 x Dt-2
Also to be noted :
Absolute deviation at period t = Absolute difference between Forecasted value during period t and Absolute value during period t
Following table accordingly calculates all forecasted values and Actual deviation values :
Year
Demand
Exponential smoothing forecast ( alpha = 0.6)
Absolute Deviation
Exponential smoothing forecast ( alpha = 0.9)
Absolute Deviation
Forecast - Regression
Absolute deviation
2 year moving average
Absolute deviation
2 year weighted moving average
Absolute deviation
1
42
42
0
42
0
42.4
0
Year moving average
2
47
42
0
42
0
46.7
0
3
51
45
6
46.5
4.5
51
0
44.5
6.5
45
6
4
56
48.6
7.4
50.55
5.45
55.3
0.7
49
7
49.4
6.6
5
59
53.04
5.96
55.455
3.545
59.6
0.6
53.5
5.5
54
5
Total =
19.36
13.495
1.3
19
17.6
It is to be noted that , Mean Absolute Deviation ( MAD) = Sum of Absolute Deviations / 3 (as number of observations )
Since Absolute deviation value of 1.3 under Linear regression forecast is least amongst all options, corresponding MAD also will be the last
The MAD for Linear Regression Forecast = 1.3/ 3 =0.433
IT SHOULD CHOOSE TREND PROJECT WITH REGRESSION AS DESIRED FORECASTING METHOD
Year
Demand
Exponential smoothing forecast ( alpha = 0.6)
Absolute Deviation
Exponential smoothing forecast ( alpha = 0.9)
Absolute Deviation
Forecast - Regression
Absolute deviation
2 year moving average
Absolute deviation
2 year weighted moving average
Absolute deviation
1
42
42
0
42
0
42.4
0
Year moving average
2
47
42
0
42
0
46.7
0
3
51
45
6
46.5
4.5
51
0
44.5
6.5
45
6
4
56
48.6
7.4
50.55
5.45
55.3
0.7
49
7
49.4
6.6
5
59
53.04
5.96
55.455
3.545
59.6
0.6
53.5
5.5
54
5
Total =
19.36
13.495
1.3
19
17.6