Exponential Smoothing and Actual Value

Q1. Sales of a particular product (in thousands of dollars) for the years 2009 through 2012 havebeen $48,000, $64,000,$67,00 and $83,000, respectively
a) What sales would you predict for 2013, using a simple four-year moving average?

F2013 = = $65,500
$65,000 is the forecast for 2013
b) What sales would you predict for 2013, using a weighted moving average with weights of0.50 for the immediate preceding year and 0.3, 0.15, and 0.05 for the three years before that?

F2013 = 0.50A2012 + 0.3A2011 + 0.15A2010 + 0.05A2009 =0.50(83000) + 0.30(67000) + 0.15(64000) + 0.05(48000) = 41,500 + 20,100 + 9,600 + 2,400 = $73,600
$73,600 is the forecast for 2013

Q2. Using exponential smoothing with a weight of 0.6 on actual values:
a) If sales are $45,000 and $50,000 for 2010 and 2011, what would you forecast for 2012?
(The first forecast is equal to the actual value of the preceding year.)
Actual values are
2010: $45,000
2011: $50,000 α = 0.6

F2012 = 0.60A2011 + 0.40A2010
= 0.60(50000) + 0.40(45000) =48000
Forecast for 2012 is $48,000
b) Given this forecast and actual 2012 sales of $53,000, what would you then forecast for2009?
Actual value of 2012 = $53,000

F2009 =

Q3. In question 4-1, taking actual 2009 sales of $48,000 as the forecast for 2010, what sales would you forecast for 2011, 2012, and 2013, using exponential smoothing and a weight a on actual values of (a) 0.4 and (b) 0.8?
a) α = 0.4
Actual values of 2009 = $48,000 and it is forecasted for 2010
We have an Actual value for 2010 = $64,000
F2011 = 0.4(64,000) + 0.6(48,000) F2011= $54,400
Now we have both actual and forecasted values for 2011
Actual value for 2011= $67,000
F2012 = 0.4(67,000) + 0.6(54,000) F2012=59,440
Now we are having both actual and forecasted values for 2012
Actual value for 2012 = $83,000
F2013 = 0.4(83,000) + 0.6( 59,440)
F2013=68,864

b) α = 0.8
Actual values for 2009 = $48,000 and is forecasted for 2010
We have Actual values for 2010 = $ 64,000
F2011 = 0.8(64,000) + 0.2(48,000) F2011=60,800
Now we have both actual and forecasted values for 2011
Actual value for 2011 = $67,000
F2012= 0.8( 67,000) + 0.2(60,800) F2012= 65,760
Now we have both actual and forecasted values for 2012
Actual value for 2012 = $83,000
F2013 = 0.8(83000) + 0.2( 65,760) F2013= 79,552

Q4. In question 4-1, what sales would you forecast for 2013, using the simple regression (leastsquares) method?
The forecast for the year 2013 can be calculated using

We should have data for regression calculation
Year
I
D
DI
I*I
2009
0
48,000
0
0
2010
1
64,000
64,000
1
2011
2
67,000
13.4000
4
2012
3
83,000
24,9000
9
Total
I=6
D=26,2000
DI=44,7000
I*I=14

Now b=
=
=10800
Where a= =65,500 = 16,200
(65500-16200) = 49,300
Forecast for 2009= 49,300 + 43,200 = 92,500
F2013 = 92,500

MISSION AND VISSION